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Everything you need to know about Soil Engineering. This article includes useful study notes on Soil Engineering for civil engineering students!

** 1. Notes on the Index Properties of Soils:**

Index properties of soils is useful in estimating the general nature of fine-grained soils. The are five main index properties of soils generally used are discussed in this article. They are: 1. Plasticity Index 2. Liquidity Index 3. Consistency Index 4. Toughness Index 5. Activity.

**1.** **Plasticity Index: **

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**It is the numerical difference between the liquid limit and the plastic limit of the soil: **

I_{p} = ω_{L }– ω_{P} …(5.6)

where I_{P} is the plasticity index, ω_{L} is the liquid limit, and ω_{P} is the plastic limit.

Plasticity index gives the range of water content over which the soil remains in the plastic state. It is one of the most important properties of the soil and forms the basis for soil classification. In the case of sandy soils, the plastic limit is first determined. When the soil cannot be molded to form a ball and rolled into a thread, the plasticity index is reported as non-plastic. When the plastic limit is equal to or greater than the liquid limit, the plasticity index is reported as zero.

**2. Liquidity Index: **

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The liquidity index is defined as the ratio of the numerical difference between natural water content and plastic limit to the plasticity index of the soil. It can be mathematically expressed as –

I_{L} = ω_{n }– ω_{P}/I_{P} …(5.7)

where I_{L} is the liquidity index, ω_{n} is the natural water content, ω_{P} is the plastic limit, and I_{P }is the plasticity index (ω_{L }– ω_{P}). Table 5.2 gives the various states of consistency of soils for different values of liquidity index.

**3. Consistency Index: **

Consistency index is defined as the ratio of the numerical difference between liquid limit and natural water content to the plasticity index of the soil. It can be mathematically expressed as –

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I_{C }= ω_{L }– ω_{n}/I_{P }…(5.8)

where I_{C }is the consistency index. Table 5.2 gives the various states of consistency of soils for different values of consistency index.

**4. Toughness Index: **

Toughness index is defined as the ratio of plasticity index and flow index. It can be mathematically expressed as –

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I_{T} = I_{P }/I_{f} …(5.9)

where I_{T} is the toughness index, I_{P} is the plasticity index, and I_{f }is the flow index. Toughness index indicates the shear strength of the soil at its plastic limit.

**5. Activity: **

Activity is defined as the ratio of plasticity index of a clay soil to the percent clay fraction. It is given by –

A = Plasticity index/% Clay fraction = I_{P}/C

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Percent clay fraction is the percentage of soil having particles finer than 0.002 mm. It can be determined by either hydrometer or pipette analysis. High activity for a given soil indicates that for the given clay fraction, the soil has high plasticity index. Activity of a soil depends on the type of clay mineral present in the soil. Figure 5.8 shows the plasticity index of three common clay minerals as a function of % clay fraction.

For any given clay fraction, the montmorillonite clay mineral shows highest plasticity index and kaolinite shows the least plasticity index. Illite shows medium plasticity index as compared to kaolinite and montmorillonite. Also, the montmorillonte shows higher increase of plasticity index (as indicated by the slope of the line) compared to those of illite and kaolinite. Thus, the activity, that is, the slope of plasticity index and percent clay fraction of montmorillonite (A_{1}) is highest compared to that of illite (A_{2}) and kaolinite (A_{3}).

Table 5.3 shows the activity of common clay minerals. Soils contain a mixture of clay and non-clay minerals and they are classified based on activity as shown in Table 5.4.

Highly active clay minerals such as montmorillonite show relatively high increase in plasticity index for a given increase of % clay. Though there is no direct relation, active minerals cause high compressibility, shrinkage, and swelling. Soils of the same geological origin generally have the same level of activity.

2. Notes on the Grain Size Distribution Curve (Soil Mineralogy):

**Construction of Grain Size Distribution Curve: **

The results of the grain size analysis, including sieve analysis and sedimentation analysis, are plotted on a graph, with particle size on the x-axis on a log scale and cumulative % finer on the x-axis on an arithmetic scale. The curve obtained is known as the grain size distribution curve.

In grain size distribution curve, the particle size is plotted on a log scale, as it varies over a wide range, from 0.002 mm to over 10 mm; so, better representation is given for all particle sizes on a log scale. Scale problems arise while plotting particle size on an arithmetic scale. If a small scale is used, small particle sizes such as 0.002 and 0.02 mm will get plotted so close to each other that they will no longer be distinguished as different points.

If a large scale is used, the graph will exceed the limits of the paper. Further, soils having the same degree of uniformity will have the same shape of the grain size distribution curve, irrespective of actual particle sizes, when it is plotted on a log scale. The grain size distribution curve is also known as particle size distribution curve or gradation curve.

The grain size distribution curve is very useful to determine the gradation of soil and to classify the soil. Gradation is the distribution of various particle size ranges in a soil.

**Deductions from Grain Size Distribution Curves****: **

Figure 6.14 shows the grain size distribution curve for a typical soil. Particle sizes corresponding to 10%, 30%, and 60% cumulative percent finer (CPF) are read from the curve, which are called D_{10}, D_{30}, and D_{60}, respectively.

% Gravel = 100 – CPF corresponding to 4.75-mm size

% Fines = CPF corresponding to 75-µm size

% Sand = 100 – (% gravel + % fines)

where CPF is cumulative percent finer.

Two parameters are used to determine the gradation of soils. First is the uniformity coefficient –

C_{u} = D_{60}/D_{10 }…(6.19)

and the second is the coefficient of curvature –

C_{c} = [D_{30}^{2}/(D_{60}× D_{10})]_{ }…(6.20)

Coarse-grained soils are classified as well-graded or poorly graded soils depending on the values of C_{u} and C_{c}, as shown in Table 6.5.

**Characteristics of Grain Size Distribution Curves****: **

Figures 6.15(a) and (b) show the grain size distribution curves of six typical soils.

**Following are the characteristics of grain size distribution curves: **

1. A curve with a gentle slope and spread across the entire particle size range represents a well-graded soil.

2. A curve with a sleep slope and extending over either sand size or gravel size represents a uniformly or poorly graded sand or gravel, respectively.

3. A curve that has a horizontal portion over any size range indicates that particles of that size range are not present in the soil and such soils are called gap-graded soils.

4. A curve situated in the top-left portion of the plot indicates a fine-grained soil, whereas a curve situated in the right portion indicates a coarse-grained soil.

5. Soils with same gradation characteristics will have parallel grain size distribution curves.

The higher the uniformity coefficient, the larger is the range of particle sizes present in the soil. If C_{u }< 2, the soil is termed as uniformly graded soil. The coefficient of curvature gives an idea of the shape of the grain size distribution curve.

**3. Notes on the Type of Water Present in Soil (Physical Properties of Soils):**

The water present in a soil mass may be of the following types: 1. Free Water 2. Capillary Water 3. Adsorbed Water 4. Structural Water.

**1. ****Free Water:**

The water present in the voids of a soil mass which is free from the physicochemical forces of attraction, repulsion, and all other forces and also free to flow against gravity under a hydraulic head is known as free water. Free water completely evaporates when the wet soil sample is heated in an oven at a temperature of (105 ± 5)°C. The pressure at any point in free water is equal to the hydrostatic pressure.

**2. ****Capillary Water: **

Capillary water is similar to free water except that it is held in the voids of a soil mass by capillary action due to surface tension forces above the groundwater table. The pressure at any point in the capillary water is negative proportional to the water’s height above the groundwater table. Capillary water also evaporates when the soil sample is heated in an oven. Capillary water cannot flow in soils because of low pressure below the atmospheric pressure, since flow takes place only from higher pressure to lower pressure.

**3. ****Adsorbed Water: **

Water that is held to the surface of clay particles by physicochemical forces of attraction and repulsion between them is known as adsorbed water. Soil Structure and Mineralogy, adsorbed water is a part of the diffuse double layer, which is formed on the surface of clay particles due to factors such as isomorphous substitution, negative surface charge, and cation exchange. The density and viscosity of adsorbed water are found to be somewhat different from those of normal water.

The properties and thickness of the film of adsorbed water on the clay particle surface depend on several factors such as cation exchange capacity of the soil, specific surface, ion size and ion valence, electrolyte concentration of the fluid as well as the size of the individual clay particle, and the nature and magnitude of the bonding forces between individual or groups of particles.

As adsorbed water is strongly held to the surface of clay particles, it cannot participate in the groundwater flow. Adsorbed water decreases the effective void space available for fluid flow and hence the thicker is the adsorbed water layer in a clay soil, the lesser is the rate of flow of water through the soil. Adsorbed water also gets evaporated on heating the soil sample in an oven at a standard temperature. The thickness or mass of adsorbed water in soil is not permanent but changes with the changes in the environment of the soil-water system.

**4. ****Structural Water:**

The water that is chemically combined in the mineral structure of the soil by bonding forces is known as structural water. Structural water cannot be removed from the soil without breaking the soil’s mineral structure. In fact, structural water exists in the mineral structure in the form of hydrogen (H^{+}) and hydroxyl (OH^{+}) ions, which are held together by hydrogen bonds.

Heating the soil sample in an oven at a standard temperature of (105 ± 5)°C does not cause any evaporation of this structural water. Uncontrolled heating of the soil sample in a sand bath or on a stove or by igniting the soil after mixing with alcohol, as used in some of the crude methods of water content determination, causes loss of structural water from the solid particles. Oven temperatures of more than 300°C are necessary to remove structural water.

In the oven-drying method of water content determination, the soil sample is heated at a standard temperature of (105 ± 5)°C to prevent evaporation of structural water. Therefore, in defining the term “water content,” the mass of structural water is used as the denominator along with the mass of the soil solids. Structural water is, thus, considered an integral part of the solid particles of soil in geotechnical engineering.

**5. ****Hygroscopic Water: **

The water which an oven dried soil sample absorbs from the atmosphere over a period of time is known as hygroscopic water.

**4. Notes on the Phreatic Line in Earth Dams (Seepage Analysis):**

The top flow line within an earth dam section separating the saturated and unsaturated zones, below which there are positive hydrostatic pressures, is known as “phreatic line.” To draw the flow net for earth dams, it is essential to locate the phreatic line, which is one of the boundary flow lines.

**1. Graphical Method****:**

Flow through the body of an earth dam is the case of unconfined seepage in which the upper boundary of the flow net is the phreatic line. The phreatic line can be located by a graphical method suggested by Casagrande.

Casagrande’s method is based on Kozeny’s analytical method for flow net for the case of water flowing above an impervious, infinite, and horizontal plane, which becomes permeable at a certain point, shown in Fig. 10.16. Kozeny’s solution consists of a family of confocal parabolas, representing the flow lines and equipotential lines. The point where the floor becomes permeable represents the focus of the parabolas.

**The procedure for locating the phreatic line in Casagrande’s graphical method is as follows: **

i. Referring to Fig. 10.17, AB is the upstream slope of the earth dam, L is the horizontal projection of the upstream slope on the water surface. Measure a distance BC = 0.3l on the water surface. Then, point C is the starting point of the base parabola.

ii. The directrix of the parabola is obtained by using the principle that any point on the parabola is equidistant from the focus and the directrix. Hence, with C as the center and CF as the radius, draw an arc to cut the horizontal line through CB in D. Draw a vertical at D. Evidently, CD = CF, and hence, the vertical line DH is the directrix.

iii. The last point, G, of the parabola will lie midway between F and H.

iv. Intermediate points on the parabola are located by using the principle that those points are equidistant from the focus F and the directrix DH (PF = QH). To locate a point P on the parabola, a vertical line QR is drawn at any distance x from F. Measure QH. Now, with F as the center and QH as the radius, draw an arc to cut the vertical line QH in P. Similarly, other points on the base parabola can be located. Join all these points to get the base parabola.

v. A correction is applied to the starting point of the base parabola to get the actual phreatic line. The phreatic line must start from B and not from C. Furthermore, AB is an equipotential line having a content head H. The phreatic line, which is the top flow line, must be perpendicular to AB. Hence, the portion of the line at B is sketched free hand in such a way that it starts at B perpendicular to AB and joins the base parabola by a smooth curve without any kink. The phreatic line must also meet the downstream filter (an equipotential line) perpendicularly (i.e., vertically) at G.

**2. Analytical Method****: **

The equation of the phreatic line (base parabola of Kozeny’s solution) can be obtained by considering any point P on it with coordinates (x, y) with respect to the focus F as origin. From the property of the parabola, PF = QH. Now –

√x^{2} + y^{2} = QF + FH

Hence, –

√x^{2} + y^{2} = x + s …(10.39)

where s = FH = focal distance. Squaring both sides of Eq. (10.39) we have –

x^{2} + y^{2 }= (x + s)^{2} Þ x^{2} + y^{2} = x^{2}+ s^{2} + 2xs Þ y^{2 }= s^{2} + 2xs …(10.40)

This is the equation of the parabola. The focal distance can be determined either graphically or calculated analytically by considering the coordinates of point C, as follows. From Eq. (10.39) –

At C, x = D and y = H. Therefore –

Equation (10.40) can be used to compute the various values of y for different values of x with focus F as origin. Now, by Darcy’s law, q = kiA –

Differentiating w.r.t. x, we get –

Substituting the value of dy/dx in Eq. (10.42), we get –

Substituting the value of y from Eq. (10.43) in Eq. (10.44), we have –

Hence, the discharge or seepage loss through the body of an earth dam can be computed from Eq. (10.45).

**5. Notes on the Design of Graded Filter (Seepage Analysis): **

A graded filter is provided in earth dams to permit the flow of water without movement or erosion of soil particles. It consists of layers of pervious material, particles being coarser in successive layers in the direction of flow.

**The following are the criteria for the design of graded filters: **

1. The filter material should be coarse enough so that the percolating water moves easily without building up pore pressures. For the filter to provide free drainage, its permeability should be at least 25 times the permeability of the base material (soil for which the filter is provided).

Since permeability is a function of the square of particle size, the ratio of particle diameters should be at least 5 –

D_{15f} > 5 x D_{15b} …(10.48)

where D_{15f} is the particle size corresponding to 15% cumulative percentage finer of the filter material and D_{15b} is the particle size corresponding to 15% cumulative percentage finer of the base material.

2. The filter material should be fine enough so that soil particles of the base material are not washed through the filter. For this condition –

D_{15f }< 5× D_{85b }…(10.49)

where D_{85b} is the particle size corresponding to 85% cumulative percentage finer of the base material.

3. In a graded filter, each layer is designed considering the layer as a filter and the preceding layer as the base material in the direction of flow. The particle size of successive filter layers increase in the direction of flow.

4.** **The material of the last layer of the filter should be coarse enough so that it is not carried away by the flow through the openings of the perforated drainage pipe. For this condition –

D_{85f}/d > 1.2 (for drainage pipes with circular perforations) …(10.50)

D_{85f} > 1.4 (for drainage pipes with slotted perforations) …(10.51)

where d is the diameter of the circular perforations of the drainage pipe and b is the width of the slot in the drainage pipe.

5. The grain size curve of the filter material should be roughly parallel to that of the base material.

6. To avoid segregation, the filter should not contain particles larger than 75 mm.

7. For proper working, the filter should not contain more than 5% fines passing through a 75-µm IS sieve.

8. The thickness and area of filter should be large enough to carry the seepage discharge safely.

9. If the filter has to work as a loaded filter, the total thickness should be large enough to provide the required weight.

**6. Notes on Flow Net (Seepage Analysis)****:**

The solution of the Laplace equation for a two-dimensional flow through soil gives two sets of functions known as velocity potential and stream function, which are together known as conjugate harmonic functions. A graphical representation of the solution of the Laplace equation gives two sets of curves known as equipotential lines and stream (or flow) lines, which are orthogonal to each other.

Equipotential lines are the lines joining points of equal potential or hydraulic head. A stream line is a line, a tangent to which at any point gives the direction of velocity at that point. A network of flow lines and equipotential lines for a given flow problem is known as a flow net.

#### Properties of Flow Net:

**Properties of flow net are as follows: **

i. Flow lines and equipotential lines are at right angles to each other.

ii. The fields are curvilinear squares such that a circle can be drawn touching all the four sides of the square.

iii. The quantity of water flowing through each flow channel is the same. Similarly the same potential drop occurs between two successive equipotential lines.

iv. Smaller the dimensions of the field, greater will be the hydraulic gradient and velocity of flow through it.

v. Flow lines cannot intersect an impermeable boundary.

vi. Equipotential lines meet an impermeable boundary at right angles.

vi. An impermeable rock or concrete surface forms a boundary flow line for the flow net.

vii. In homogeneous soils, every transition or change in direction in the shape of curves is smooth being either elliptical or parabolic in shape.

**Methods of Drawing a Flow Net****:**

**There are several methods available for the construction of flow net, some of which are as follows: **

1. Graphical method.

2. Electrical analogy method.

3. Earth dam model method.

4. Mathematical method.

5. Analytical method.

The graphical method has been explained in the following subsection.

**1. Graphical Method****: **

It is the simplest method of flow net construction and is based on trial sketching. The method consists of first identifying the boundary conditions for the given flow problem and then drawing the flow lines and equipotential lines, duly observing the properties of a flow net.

**Important boundary conditions used in the graphical method are the following: **

i. All impermeable surfaces, for example, concrete or rock surfaces, are boundary flow lines and equipotential lines must meet them at right angles.

ii. The topmost soil surface is boundary equipotential line and flow lines must start at right angles from it.

**The following points must be kept in mind while sketching a flow net: **

i. Four or five flow channels are usually sufficient for the first attempt. The use of too many flow channels may distract the attention from essential features.

ii. The appearance of the entire flow net must be always watched and not just a part of it. Smaller details can be adjusted after the entire flow net has been roughly drawn.

iii. The curves forming the flow net should be roughly elliptical or parabolic in shape and all transitions should be smooth without any kink.

iv. The flow lines and equipotential lines are orthogonal and form approximate curvilinear squares.

v. The size of the field decreases gradually from the upstream side and then increases gradually toward the downstream side.

A reasonably good flow net can be drawn by the graphical method even by a beginner with some practice. The accuracy of the hydraulic parameters, such as discharge and seepage pressure computed from a flow net, does not depend much on the accuracy of the flow net. A reasonably good estimate of the hydraulic parameters can be therefore made even from a rough flow net.

The graphical method of flow net construction is therefore the most used method, although it is based on trial sketching. Figures 10.10 and 10.11 show the example of flow net for a weir and a concrete dam, respectively, drawn using the graphical method.

**Flow Net for Anisotropic Soils****: **

For flow through an anisotropic soil, permeabilities in the horizontal (k_{x}) and vertical directions (k_{z}) are different, and the equation of flow can be expressed as –

Equation (10.33) is not a Laplace equation and hence the principles of flow net construction are not applicable to an anisotropic soil. It can be converted into the Laplacean form by transforming the x-coordinate as –

Equation (10.33) can be therefore written as –

Equation (10.35) is in the Laplacean form in terms of x_{t} and z. Hence, the principles of flow net construction can be used for an anisotropic soil after transformation of the hydraulic structure from the (x, z) – to the (x_{t,} z)-coordinate system.

Hence, to draw the flow net for a hydraulic structure in an anisotropic soil, the transformed section of the structure is drawn, keeping the z-scale unchanged but reducing the x-scale by the ratio x_{t} = x . √k_{z}/k_{x} .

The flow net is constructed for the transformed section, as shown in Fig. 10.14, by any of the usual methods. The flow net for the original section is then obtained by retransforming the cross-section including the flow net back to the natural scale by multiplying the dimensions in the X-direction by √k_{x}/k_{z}, as shown in Fig. 10.15.

The actual flow net for anisotropic soil, thus, will not have an orthogonal set of curves, consisting of curvilinear rectangles instead of curvilinear squares. The field of the transformed section will be a curvilinear square, while the field of the actual section (retransformed) will be rectangular, having its length in the X-direction equal to √k_{x}/k_{z} times the width in the Z-direction. For the flow net of the transformed section, we have –

Since the quantity of flow should be the same for both the transformed section and the original section, equating the two, we have –

Hence, the discharge through the flow net is given by –

**7. Notes on Pre-Compression and Pre-Consolidation Pressure in Soil (Soil Consolidation): **

Pre-compression is the decrease in volume by consolidation that has taken place in a soil mass due to loads which existed on the soil mass in the past but were later removed due to various causes.

**Meaning of Pre-Compression****: **

Soil is a plastic material. Major part of the compression (deformation) of the soil, caused by the stresses, is permanent and is not recovered if the stresses are removed due to some reason. Only a small part of the compression may be recovered when the stresses are removed.

A soil deposit that undergoes at least one cycle of stress application followed by stress release is said to have undergone pre-compression.

**Causes of Pre-Compression****: **

**Pre-compression in clays may be caused due to the following reasons: **

1. Demolition of existing or old structures for construction of a new structure at the same site.

2. Sustained downward seepage that causes additional seepage forces which become absent after the seepage stops.

3. Capillarity in soil causing additional stresses that may be destroyed later due to rise of GWT.

4. Overburden that has been later removed by erosion.

5. Desiccation of clay deposit.

6. Melting of glaciers covering a soil deposit.

7. Movement of earth’s crust due to tectonic forces.

**Pre-Consolidation Pressure****: **

The maximum pressure under which a soil has been consolidated in its past stress history due to pre-compression is known as pre-consolidation pressure.

**The pre-consolidation pressure of a soil deposit can be estimated from the e-log****σ**** ‘curve using the following procedure suggested by Casagrande: **

1. Conduct a consolidation test on the undisturbed soil specimen obtained from the soil deposit and draw the e-logσ ‘ curve as shown in Fig. 11.24.

2. Locate the point E on the e-logσ’ curve, where the curvature is maximum or the radius is minimum.

3. Draw a tangent ET to the curve at the point E.

4. Draw a horizontal line EH from the point E.

5. Measure the angle HET and draw a line ER, bisecting this angle HET from the point E.

6. Extend the straight line portion CD of the e-logσ’ curve backward to intersect the bisector ER at point P.

7. The abscissa (x-coordinate) of the point P gives the value of pre-consolidation pressure on the log scale.

**8. Notes on the Compression or Settlement of Soils (Soil Compaction):**

**Depending on the type of soil, compression or settlement of soils under loads can consist of three components which are discussed below: **

**1. Initial Compression****: **

When a load is applied on a soil specimen, a decrease in the volume occurs almost instantaneously or over a short time interval due to unevenness of the surface of the soil specimen or due to expulsion of water nearest to the surface of the specimen or due to expulsion of air in case the soil is not fully saturated. This compression of the soil, which occurs due to unevenness of the surface or due to expulsion or air due to unsaturation or due to expulsion pore water from near the surface of the specimen, is called initial compression.

Initial compression is not part of consolidation and hence is excluded by making correction to the dial gauge reading from initial dial gauge reading to corrected zero dial gauge reading in the time fitting methods of determining the coefficient of consolidation.

**2. Primary Compression****: **

After the initial compression of the soil, the decrease in the volume of soil that occurs due to expulsion of pore water under sustained load is known as primary compression or consolidation. The stage of primary compression or consolidation is marked by decrease in the pore water pressure from the initial value equal to the applied stress increment to the final value of zero.

All the time-settlement calculations with coefficient of consolidation and time factor applying Terzaghi’s theory of consolidation are applicable only to the primary compression.

In fine-grained soils, primary compression occurs over considerable time ranging from a few months to several years and depends on the permeability of the soil and the availability of drainage faces. In coarse-grained soils, primary compression is completed quickly due to high permeability of soil and because there is no need for a drainage face; it is often completed during the construction of the structure.

**3. Secondary Compression****: **

As per Terzaghi’s theory of consolidation, the primary consolidation stops when the dissipation of excess pore water pressure ceases and excess pore water pressure becomes zero. However, in actual practice, compression of certain soils is found to continue even after the full dissipation of excess pore water pressure. This part of the compression that occurs under constant effective stress, even after the excess pore water pressure becomes zero, is known as secondary compression or consolidation.

The causes of secondary consolidation are attributed to the gradual rearrangement of soil particles when the full effective stress is mobilized. It is also attributed to the progressive fracture of inter-particle bonds and the fracture of some of the weak particles. Terzaghi’s theory of consolidation cannot be applied for time-settlement computations in the secondary consolidation range.

As there is no involvement of expulsion of pore water and dissipation of pore water pressure, the magnitude of secondary compression is a function of time alone as given by –

where C_{t} is the secondary compression index, e_{p} is the void ratio corresponding to 100% primary consolidation, and t_{1} and t_{2} are the time intervals.

The secondary compression index C_{t} is the slope of the e-logT curve (Fig. 11.28) in the secondary compression range. It is given by the expression –

C_{t} = Δe/log (t_{2}/t_{1}) …(11.52)

The secondary compression index decreases with increase in the thickness of the clay layer. In thick clay layer, the primary consolidation is completed quickly near the drainage face, and secondary consolidation starts while primary consolidation continues to take place at the center of the clay layer. The secondary compression index is also found to decrease with increase in the stress increment ratio Δσ’/σ’_{0}.

Secondary compression is significant for highly plastic clays, organic soils, and for loosely deposited clays and micaceous silts. In some organic soils, the secondary compression may be very large and more significant than primary compression. In over-consolidated inorganic clays, secondary compression is relatively small and is neglected.

**Compression Ratios:**

There are three types of compression ratios to know the relative magnitude of initial, primary, and secondary compression.

**They are defined further and can be calculated for every effective stress increment from the time-dial gauge readings: **

Initial compression ratio –

Primary compression ratio –

Secondary compression ratio –

where R_{0} is the initial dial gauge reading in the given stress increment, R_{c} the corrected zero dial gauge reading, and R_{f} the final dial gauge reading in the given stress increment.

**9. Notes on the Prediction of Filed Consolidation Curve (Soil Consolidation)****: **

Terzaghi’s theory of consolidation implicitly assumes that the load is applied instantaneously on the soil. Even in the laboratory consolidation test, each stress increment is applied instantaneously on the soil specimen.

In actual construction of the structure, major part of the dead load is applied rather than gradually extending over the period of construction. For construction of foundation or substructure, excavation of the soil is done, which decreases the stress in the pressure bulb zone of the soil. The foundation is then constructed that increases the stress increment gradually to zero and thereafter additional stress is exerted on the soil greater than the existing stress due to overburden. When the construction of the structure is completed, the stress on the soil gradually increases from zero to maximum stress over the period of construction.

The time-settlement curve, which is obtained from the laboratory consolidation test data applying the Terzaghi’s theory of consolidation, therefore requires correction for construction period.

Figure 11.29(a) shows the load on the soil as a function of time. As the load decreases due to excavation, the net load on the soil becomes zero in time, say t = t_{0}. It gradually increases to full load in time t = t_{c}, where t_{c} is the loading period. During the time t = 0 to t = t_{0}, there is expansion of soil due to stress release followed by re-compression. It is assumed that the net compression of soil during time t = 0 to t = t_{0} is negligible. The actual loading period is then from t = t_{0} to t = t_{c}, during which the load is assumed to increase linearly from zero to the full load P.

**Procedure for Obtaining Corrected Time-Settlement Curve****: **

The corrected time-settlement curve is obtained by plotting a graph between settlement versus time assuming that the load P is applied instantaneously at the middle of the loading period, that is, at time t = t_{c}/2.

1. The instantaneous ‘time-settlement curve as obtained from the laboratory consolidation test is shown in Fig. 11.29(b) as OABCDEFGH. This curve is now to be corrected for loading or construction period to get the field consolidation curve.

2. As the load is assumed to be instantaneously applied at time t_{c}/2, the points D, E, F, G, and H are shifted horizontally by a distance t_{c}/2 to obtain the points D’, E’ F’, G’, and H’ on the corrected settlement curve.

3. Correction for the consolidation curve at any time t < t_{c}/2 is done by reducing the load proportionately, relative to the full load at time t = t_{c}. For this, draw a vertical line Y_{1} – Y_{1} at time t = t_{c}.

4. Draw a horizontal line from any point A on the instantaneous load-settlement curve to intersect the vertical line Y_{1} – Y_{1} at point A_{1}.

5. Draw a line joining the points A_{1} and origin O.

6. Draw a vertical line at point A to intersect the line OA_{1} at A’. Point A’ is the required corrected point on the field consolidation curve for point A.

7. In a similar way, the points B and C are corrected to obtain the points B’ and C, respectively.

8. Join the points O, A’ B’ C’, D’, E’ F’ G’, and H’ by a smooth curve to obtain the field consolidation curve.

### 10. Notes on the Compaction Curves for Soil and Sand (Soil Compaction):

**Ideal Compaction Curve-Zero Air Void Line****: **

As the main objective of compaction is to increase the dry density by reducing the air voids, the ideal compaction would represent a condition where the air voids are reduced to zero by compaction. The dry density corresponding to zero air voids is the maximum possible dry density achievable by compaction and is known as theoretical MDD.

**Consider the expression for the dry density in terms of air voids: **

The expression for theoretical MDD can be obtained by substituting percent air voids, n_{a} = 0, in Eq. (12.3). Thus –

As for a given soil, the specific gravity (G) and density of water (γ_{w}) are constant. Equation (12.4) gives a relationship between theoretical MDD and water content and this relationship can be plotted on the same compaction curve that is used to determine OMC. Such a curve that represents a relationship between theoretical MDD and water content is known as zero air void line (ZAVL).

It gives the maximum possible dry density at any given water content. Figur=e 12.4 shows zero air void line or ideal compaction curve. It may be noted that any laboratory or field compaction methods cannot remove the air voids completely. Thus, the theoretical MDD represents a hypothetical and ideal case.

At any given water content, when certain level of dry density is achieved by compaction, the soil still contains some air voids. Saturation of the compacted soil by wetting with water for sufficient time may cause the air voids to be filled with water, but this increases the water content and bulk density without increasing the dry density further.

The theoretical MDD represents a case where the MDD already achieved by compaction is further increased to the theoretical maximum value by complete removal of air voids by additional compaction. As there are no air voids in the case of soil with theoretical MDD, it represents a 100% saturation condition. Thus, ZAVL is also known as 100% saturation line.

**Compaction Curve for Sands****: **

The lubricating mechanism of water forming a film around soil particles, causing them for a closer packing and consequent increase of dry density with increase in the water content, occurs only in the case of soils containing at least some percentage of cohesion or clay fraction. For pure sands or coarse-grained soils, there is no lubricating effect of water on soil particles and hence no definite relationship exists between dry density and water content for such soils.

The compaction curve for pure sands or coarse-grained soils shows only scattered points without a distinct value of optimum water content. In fact, increase of water content in sands initially decreases the dry density due to bulking of sand as shown in Fig. 12.7. This is due to capillary tension of pore water that prevents closer packing during compaction. The minimum dry density occurs at a water content of about 4%-5% due to bulking of sand.

When water content increases further, the capillary tension of the pore water is destroyed, and this allows the particles to a pack closely during compaction. The MDD occurs when the soil becomes fully saturated. If the water content is increased beyond this point, the dry density decreases again.

As there is no distinct optimum water content for sands, laboratory compaction test cannot give any guideline regarding the optimum water content to be used for compaction in the field or the MDD to be achieved during field compaction. Thus, the compaction test is of little practical use for sands. To overcome this difficulty, the relative density is used as a measure to determine the effectiveness of compaction.

The maximum and minimum void ratios of sand in the loosest and the densest state are first determined in the laboratory. The in-situ void ratio (e) of the soil is determined in the field after compaction. The relative density is then determined from the expression –

### 11. Notes on the Typical Values of Friction Angle of Soils (Shear Strength):

**Typical Values of Drained Strength for Sands:**

Table 13.4 gives typical values of friction angle for sands under drained conditions.

**Critical Void Ratio: **

For loose saturated sand in a shear test, the volume of the soil specimen decreases with increase in shear strain and finally the specimen reaches constant volume. The decrease in the volume of loose sand during shear produces positive excess pore pressures, reducing the effective stress and shear strength.

In case of dense saturated sand, the volume of the soil specimen increases after some initial adjustment with increase in shear strain and finally attains some constant volume. The increase in volume causes negative pore pressure increasing the shear strength.

If sand with an initial void ratio corresponding to the constant volume is subjected to shear, the volume of the soil specimen does not change and hence no excess pore pressures are developed during shear.

This void ratio at which cohesionless soils do not undergo any volume change during shear is known as CVR.

As the soil with initial void ratio of CVR does not undergo any volume change during shear, no pore pressures are developed and the shear strength of the soil is the same in CU and CD tests.

The CVR can be determined by conducting shear tests on sands of different relative density and plotting a graph between volume change and void ratio. The void ratio corresponding to zero volume change gives the CVR. The CVR is useful as a threshold void ratio in compacting fine and medium sands to reduce their liquefaction potential.

**Liquefaction:**

Fine and silty saturated sands with a high void ratio undergo decrease in volume during shear, causing development of positive pore pressures. When such soils are subjected to suddenly applied loads, such as those due to earthquake, heavy blasting, and pile-driving operations, the resulting excess pore pressures cause a decrease in the effective stress. Since the shear strength of granular soil directly depends on the effective stress, it causes a sudden decrease in the shear strength.

If the shear strength decreases to a value less than the applied shear stresses, the mass of sand will fail in shear. Such a failure occurs suddenly and the whole mass of sand appears to flow laterally, as if it were a heavy fluid. This type of failure in sands is known as liquefaction and is responsible for catastrophic failure of many structures.

The soils most susceptible to liquefaction are the saturated fine and medium sands of uniform gradation. Great care is required when constructing structures over such deposits. It is known that when soils are compacted to a void ratio less than the CVR, they undergo increase in volume during shear and hence negative pore pressures are developed under suddenly applied load, increasing the effective stress and shear strength. Hence, liquefaction can be avoided by compacting the sands to a void ratio less than their CVR.

Because of the differences in strength characteristics of fine sand under static and dynamic loads, the static strength characteristics cannot be used to evaluate the stability of structures under dynamic loads. Special cyclic shear tests shall be used to determine the dynamic strength, which is usually much less than the static failure stress.

**12. Notes on Rock Core Sampling (Soil Exploration):**

Undisturbed samples of rock are obtained in the form of continuous circular cores. Samples of rock are used for identification of rock type, its mineralogy, and degree of weathering as well as for conducting laboratory tests to determine the compressive strength and other properties as per the requirements of the project.

The core drilling method is used in conjunction with the method adopted for a boring program, which may be rotary boring or percussion drilling. In this method, a core barrel, fitted with a drilling bit is attached to the bottom of the hollow drill rod. Special type of diamond-studded coring bit is used for the purpose of rock core sampling.

As the drill rod is rotated, the coring bit advances and cuts an annular hole into the rock mass, securing a circular rock core into the core barrel. The core is then removed from its bottom and is retained by a core lifter. Water is pumped continuously into the drill rod to keep the drilling bit cool and to carry the disintegrated material to the ground surface.

Usually, continuous coring is done and the rock cores are stored in a core box with depth marked corresponding to each part of the core. The quality of the rock core sampling is determined and expressed in terms of rock quality designation (RQD).

RQD is defined as the ratio of the total length of sound rock core pieces of length 10 cm or more to the total length of core run, expressed as a percentage, given by –

RQD = L_{10}/L_{c }x 100 …(14.5)

where L_{10} is the total length of the sound rock core pieces of length 10 cm or more and L_{c} the total length of the core run.

RQD is a measure of the degree of fracturing of the rock during sampling as well as the degree of the weathering of the rock. Table 14.4 shows the classification of rock quality based on RQD.

**13. Notes on the Design of Casagrande’s Piezometer for Determining Water Level (Soil Exploration):**

The position of GWT below ground level is needed for estimation of consolidation settlements and for design of foundation. As the GWT changes seasonally, it is necessary to establish the highest and the lowest water level.

The position of GWT in a test pit can be directly measured with a tape. For determining the water level in a borehole, a chalk-coated tape is lowered. The depth can also be measured by lowering the leads of an electric circuit. When the open ends of leads touch the water, the circuit is closed glowing an indicator lamp. These methods are suitable in soils of high permeability, where the water level in the borehole stabilizes within 24 h.

In soils of very low permeability, the groundwater level in the borehole does not stabilize even after several weeks. Casagrande’s piezometer may be used in such cases for location of the water level. Casagrande’s piezometer, as shown in Fig. 14.17, consists of a Norton porous tube attached to a plastic tube. The porous tube is carefully placed in a sand cushion in the bottom of the cased borehole in such a way that it extends below the bottom of the casing.

The lower end of the porous tube is plugged with a rubber stopper. At the top, the porous tube is surrounded by sand. The sand cushion in the borehole is sealed with a clay seal of impermeable bentonite. The sand surrounding the porous tube should be kept saturated, during and after installation of the piezometer. The groundwater level is determined from the level of the water in the plastic tube.