Course layout • Soil compaction • Stresses in soil mass due to self-weight • Stresses in soil mass due to external loads • Consolidation • Shear Strength of Soil

References • Fundamentals of geotechnical engineering, by Braja M. Das • Elements of Soil Mechanics by Smith and smith • Soil Mechanics by R F Craig

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Introduction • In the construction of highway embankments, earth dams, and many other engineering structures, loose soils must be compacted to increase their unit weights. • Compaction increases the strength characteristics of soils. • Roller compactors are generally used in the field for soil compaction.

Figure 7.1 Roller compactors General Principles of compaction • Compaction is the densification of soil by removal of air, which requires mechanical energy. • Water acts as a lubricant agent on the soil particles. So, the soil particles slip over each other and move into a densely packed position. • The dry unit weight after compaction first increases as the moisture content increases (Figure 7.2).

Figure 7.2 A Typical compaction curve

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����� ������������� ���������� • Beyond a certain moisture content w=OMC, (Figure 7.2), any increase in the moisture content tends to reduce the dry unit weight. This is because the water takes up the spaces that would have been occupied by the solid particles. • The moisture content at which the maximum dry unit weight is attained is generally referred to as the optimum moisture content. The laboratory test generally used to obtain the maximum dry unit weight of compaction and the optimum moisture content is called the Proctor compaction test. There are two types of Proctor compaction test: i. Standard Proctor Test ii. Modified Proctor Test

i. Standard Proctor Test • In the Proctor test, the soil is compacted in a mold that has a volume of 943.3 cm3, see Figure 7.3 • The soil is mixed with varying amounts of water and then compacted in three equal layers by a hammer. • Number of blows on each layer is 25. • The hammer weighs 24.4 N (mass ≈ 2.5 kg), and has a drop of 304.8 mm. For each test. • The moist unit weight of compaction can be calculated as � = ��(�) (7.1) Where � = weight of the compacted soil in the mold �(�)= volume of the mold (= 943.3 cm3)

Figure 7.3 Standard Proctor test equipment: (a) mold; (b) hammer

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����� ������������� ���������� For each test, the moisture content of the compacted soil is determined in the laboratory. With known moisture content, the dry unit weight d can be calculated as: �� = �1 + �(%)100 (7.2) where �(%) percentage of moisture content. The values of �� determined from Eq. (7.2) can be plotted against the corresponding moisture contents to obtain the maximum dry unit weight and the optimum moisture content for the soil. For a given moisture content, the theoretical maximum dry unit weight is obtained when there is no air in the void spaces—that is, when the degree of saturation equals 100%. Thus, the maximum dry unit weight at a given moisture content with zero air voids can be given by ���� = ��� + 1�� (7.3) where ���� zero-air-void unit weight �� unit weight of water �� specific gravity of soil solids To obtain the variation of ���� with moisture content, assume several values of �, such as 5%, 10%, 15%, and so on. Then use Eq. (7.3) to calculate ���� for various values of �. Figure 7.1 also shows the variation of ����. Under no circumstances should any part of the compaction curve lie to the right of the zero-air-void curve. In several instances it is more convenient to work with density (kg/m3) rather than unit weight. In that case, Eqs. (7.1), (7.2), and (7.3) can be rewritten as �(��/��) = �(��)�(�)(��) (7.4) �� = �1 + �(%)100 (7.5) ���� = ��� + 1�� (7.6) where: �,�� ,���� density, dry density, and zero-air-void density, respectively �� Density of water (1000 kg/m3) � Mass of compacted soil in the mold �(�) Volume of mold=943.3×10-6 m3

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����� ������������� ���������� Factors Affecting Compaction 1- Soil Type The soil type—that is, grain-size distribution, shape of the soil grains, specific gravity of soil solids, and amount and type of clay minerals present—has a great influence on the maximum dry unit weight and optimum moisture content. Four different types of compaction curves are observed as shown in Figure 7.4.

Figure 7.4 Various types of compaction curves encountered in soils 2- Compaction Effort The compaction energy per unit volume, E, used for the standard Proctor test described in Section 7.2 can be given as

� = ������� �� ����� ��� ������ × ������� �� ����� � × �����ℎ���ℎ������ × �ℎ���ℎ� ������ ��ℎ����� ������� �� ����

or � = (25) × (3) × (24.4 × 10�� ��) × (0.3048 �)943.3 × 10�� �� = 591.3��.�/�� If the compaction effort per unit volume of soil is changed, the moisture–unit weight curve will also change. This can be demonstrated with the aid of Figur 7.5.

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Figure 7.5 Effect of compaction energy on the compaction of a sandy clay ii- Modified Proctor Test With the development of heavy rollers and their use in field compaction, the standard Proctor test was modified to better represent field conditions. This is sometimes referred to as the modified Proctor test. (See Figure 7.6) For Fine material For coarse material 1. The volume of the mold is 943.3 cm3 [as in the case of the standard Proctor test]. 1. The volume of the mold is 2124 cm3 2. The soil is compacted in five layers. 2. The soil is compacted in five layers. 3. The hammer weight is 44.5 N (mass =4.536 kg). 3. The hammer weight is 44.5 N (mass =4.536 kg). 4. The drop of the hammer is 457.2 mm. 4. The drop of the hammer is 457.2 mm. 5. The number of hammer blows for each layer is 25 [as in the case of the standard Proctor test]. 5. The number of hammer blows for each layer is 56.

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Figure 7.6 Comparision of standard (right) and modified (left) Proctor hammers and molds The compaction energy for unit volume of soil in the modified test can be calculated as � = (25) × (5) × (44.5 × 10�� ��) × (0.34572 �)943.3 × 10�� �� = 2696 ��.�/�� Because it increases the compactive effort, the modified Proctor test results in an increase of the maximum dry unit weight of the soil. The increase of the maximum dry unit weight is accompanied by a decrease of the optimum moisture content. Example 7.1 The laboratory test data for a standard Proctor test are given in the table. Find the maximum dry unit weight and the optimum moisture content. Volume of Proctor mold (cm3) Mass of wet soil in the mold (kg) Moisture content (%) 943.3 1.48 8.4 943.3 1.88 10.2 943.3 2.12 12.3 943.3 1.82 14.6 943.3 1.65 16.8 Solution We can prepare the following table: Volume (cm3) Mass of Moist wet soil (kg) density (kg/m3) Moisture content, � (%) Dry density, ρ� (kg/m3) 943.3 1.48 1568.96 8.4 1447.38 943.3 1.88 1993.00 10.2 1808.53 943.3 2.12 2247.43 12.3 2001.27 943.3 1.82 1929.40 14.6 1683.60 943.3 1.68 1780.98 16.8 1524.81 The plot of �� against � is shown in Figure 7.7. From the graph, we observe

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����� ������������� ���������� Maximum dry density=2020 kg/m3 and Optimum moisture content =13%

Figure 7.7 Standard compaction curve of soil tested in example 7.1 Example 7.2 Calculate the zero-air-voids unit weights (in kN/m3) for a soil with Gs=2.68 at moisture contents 5, 10, 15, 20, and 25%. Plot a graph of ���� against moisture content. Solution Substitute �� = 2.68 and �� = 9.81 kN/m� in the equation ���� = ���� ��� � (%) ���� (��/��) 5 23.18 10 20.73 15 18.75 20 17.12 25 15.74 The plot is shown below

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����� ������������� ���������� Field Compaction Most compaction in the field is done with rollers. There are four common types of rollers: 1. Smooth-wheel roller (or smooth-drum roller) (for sandy and clayey soils) 2. Pneumatic rubber-tired roller (for sandy and clayey soils) 3. Sheepsfoot roller (most effective in compacting clayey soils) 4. Vibratory roller (very efficient in compacting granular soils) . Vibrators can be attached to smooth-wheel, pneumatic rubber-tired, or sheepsfoot rollers to provide vibratory effects to the soil. 5. Hand-held vibrating plates can be used for effective compaction of granular soils over a limited area.

Factors must be considered to achieve the desired unit weight of compaction in the field. 1. Soil type and moisture content. 2. The thickness of lift, 3. The intensity of pressure applied by the compacting equipment 4. The number of roller passes (about 10 to 15 roller passes yield the maximum dry unit weight economically attainable). The pressure applied at the surface decreases with depth, resulting in a decrease in the degree of compaction of soil.

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����� ������������� ���������� Specifications for Field Compaction In most specifications for earth work, one stipulation is that the contractor must achieve a compacted field dry unit weight of 90% to 95% of the maximum dry unit weight determined in the laboratory by either the standard or modified Proctor test. This specification is, in fact, for relative compaction R, which can be expressed as �(%) = ��(�����)��(�������) × 100 In the compaction of granular soils, specifications are sometimes written in terms of the required relative density �� or compaction. [Relative density should not be confused with relative compaction]. Determination of Field Unit Weight after Compaction

• When the compaction work is progressing in the field, it is useful to know whether or not the unit weight specified is achieved. • Three standard procedures are used for determining the field unit weight of compaction: 1. Sand cone method 2. Rubber balloon method 3. Nuclear method

Sand Cone Method The sand cone device consists of a glass or plastic jar with a metal cone attached at its top (Figure 7.8). The jar is filled with very uniform dry Ottawa sand. The weight of the jar, the cone, and the sand filling the jar is determined (��). In the field, a small hole is excavated in the area where the soil has been compacted. If the weight of the moist soil excavated from the hole (��) is determined and the moisture content of the excavated soil is known, the dry weight of the soil (��) can be found as �� = ��1 + �(%)100 where � moisture content. After excavation of the hole, the cone with the sand-filled jar attached to it is inverted and placed over the hole (Figure 7.9). Sand is allowed to flow out of the jar into the hole and the cone. Once the hole and cone are filled, the weight of the jar the cone, and the remaining sand in the jar is determined (W4), so �� = �� −�� Where ��= weight of sand to fill the hole and cone. The volume of the hole excavated can now be determined as

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����� ������������� ���������� � = �� −����(����) where ��= weight of sand to fill the cone only ��(����)= dry unit weight of Ottawa sand used Thus, the dry unit weight of soil is computed as �� = ���

Figure 7.8 Sand Cone tests apparatus Figure 7.9 Field unit weight by sand cone method Example 7.3 The data of sand cone test are as follows. Initial weight of the cone, jar and sand, (�� = 4320 gm). The weight of the moist soil excavated from the hole (�� = 711 gm), the moisture content � = 12% The weight of cone, jar and sand after performing the test, �� = 3017 gm. weight of sand to fill the cone, �� = 849 gm. The density of the sand, ��(����) = 1.42 gm/cm�. Determine the field density of a compacted soil using

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����� ������������� ���������� Solution The weight of the dry soil, ��, is: �� = ��1 + �(%)100 �� = 7111 + 12100 = 634.8 gm

The weight of sand to fill the hole and cone, �� is: �� = �� −�� �� = 4320 − 3017 = 1303 gm The volume, �, of the hole excavated can now be determined as � = �� −����(����) � = 1303 − 8491.42 = 319.7 cm�

The dry unit weight of soil is �� = ��� �� = 634.8319.7 = 1.98 gm/cm�

Rubber Balloon Method The procedure for the rubber balloon method is similar to that for the sand cone method; a test hole is made, and the moist weight of the soil removed from the hole and its moisture content are determined. However, the volume of the hole is determined by introducing a rubber balloon filled with water from a calibrated vessel into the hole, from which the volume can be read directly.

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����� ������������� ���������� Appendix A of chapter 7 Illustration of sand cone test procedure W1= Initial weight of the cone, jar and sand

W2= The weight of the moist soil excavated from the hole

W3, weight of the dry excavated soil Performing the experiment

W4= The weight of cone, jar and sand after performing the test

Wc= weight of sand to fill the cone

Weight of sand in the hole=�� −��

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����� ������������� ���������� Appendix B of chapter 7 Illustration of rubber balloon test