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B; A: B A sample of soil with a liquid limit of Comment on the consistency of the soil. The weight of the saturated soil was The weight and volume of the dried soil were Determine the shrinkage limit of the soil and the shrinkage ratio, Determine the shrinkage limit of the soil and its shrinkage ratio.
Laboratory tests on the sand sample indicated the void ratios in the loosest and the densest possible states as 0. For a volume of cc, the dry in the densest and loosest states are and g, respectively. Compute the relative density of sand assuming the specific gravity of solids to be 2. The minimum and maximum dry unit weight of a sand were found to be Two clay soils have the following characteristics. Calculate their activity values. Lambe, T. Skempton, A. Conf, on Soil Mech.
Zurich, Vol. Taylor, DLW. These terms, however, are too general and include a wide range of engineering properties. Hence, additional means of categorisation are necessary to make the terms more meaningful in engineering practice. These terms are compiled to form soil classification systems. A soil classification system is meant essentially to provide a language of communication between engineers. Sorting of soils into groups each of which would show similar behaviour, is the object of soill classification.
Any soil classification system must provide us with information about the probable engineering behaviour of a soil.
This means that once a soil is classified, it should be possible to grade the soil for its suitability for a specific engineering project. A classification system must be simple to use, and the number of soil groups not too many in number. The most commonly used properties are the grain-size distribution and plasticity.
However, a soil classification system does not eliminate the need for detailed soil investigations and for testing for engineering properties. It can at best give some fair idea about its engineering behaviour. Several classification systems were evolved by different organisations having a specific purpose as the object.
Casagrande describes the systems developed and used in highway enginecring, airfield construction, etc. According to the USCS, the coarse-grained soils are classified on the basis of their grain-size distribution and the fine-grained soils whose behaviour is controlled by plasticity on the basis of their plasticity characteristics. Table 3. Group symbols consisting of a prefix and a suffix are use" for various groups Table 3. Coarse-grained soils are those having 50 per cent or more retained on the No.
They are further subdivided into gravels and sands. Both gravel and sand are divided into four subgroups Table 3. Whether a soil is well-graded or poorly-graded can be determined by plotting the grain size distribution curve and computing the coefficient of uniformity, Cy and the coefficient of curvature, C,.
These coefficients are defined in Chapter 2. GW and SW groups are well-graded gravels and sands with less than 5 per cent passing sieve whereas the GP and SP groups are poorly-graded gravels and sands with little or no fines.
Fine-grained soils having more than 50 per cent material passing the no 0. These are subdivided into silt M and clay C , based on their liquid limit and plasticity index. As shown in Table 3. Silt, clay and organic fractions are further subdivided into soils possessing low L or high ff plasticity when the liquid limit is tess than 50 per cent and more than 50 per cent, respectively, ly organic soils, fibrous in nature, usually peat and swampy soils having high compressi subdivided.
These are put into one group only with group symbol, P,. The system hhas also-the field identification procedure incorporated inte it lity are not 3. The original system has been revised several times. The system is based on both the particle size and the plasticity characteristics.
The applicability of the system has also been extended considerably. The system includes several sub-groups Table 3. The group index should be rounded off to the nearest whole number. If the computed value is negative, it is reported as zero. To classify a soil, its grain-size distribution, liquid limit and plasticity index values are determined, Once these data are available, the classification is cartied out by proceeding from left to right in the chart of Table 3.
A complete classification includes the group index in parentheses. Thus, A 3 indicates a soil type A, having a group index of 3. In general, the greater the group index value, the less desirable a soil is for highway construction within that subgroup. A group index of 0 indicates a good subgrade material, while a group index of 20 or more indicates a very poor subgrade material, 3.
The laboratory classification criteria for the coarse-grained soils is the same as inthe USCS and shown in Table 3. According to Table 3. The coordinates plot above the A line on the plasticity chart, in the CH region.
It is, thus, an inorganic clay of high compressibility. Values of liquid limit and plastic limit are unusually high, These are typical data from the Mexico city clay. Hence, the soit can be assigned the dual symbol CCF. It is an inorganic clay of low to intermediate compressibility. It is an inorganic clay to silt of high compressibility.
Hence, it is a fine-grained soil. However, the soil is non-plastic and the plasticity chart cannot be used, It can, thus, classified as MZ NP ie. Hence it is a coarse-grained soil. Since a larger proportion of the coarse-grained soil is gravel, the soil is gravel. The point plots above the A-line. Soil F: It is a coarse-grained soil and the soil is sand. Since grain-size distribution is not given, the first symbol can be either SP or SW. Given the data of Fig.
Figure 3. The Atterberg limits of these soils are given below: Soil we wr lp. Casagrande, A. New Delhi. This, however, is only partly true. Incase of coarse-grained soils, the mineralogical composition of the grains hardly affects the engineering properties of the soils. Perhaps the grain to grain friction is influenced to a degree. In such soils, interparticle forces other than those due t0 gravity arc of no consequence.
But the finer the particles, the more significant become the forces associated with the surface area of the grains, The chemical character of the individual grain assumes importance especially when the surface area is large relative to the size of the grain—a condition which is associated with fine-grained soils. Thus, interparticle attraction holding the grains together becomes increasingly important as the size decreases.
Soil structure means the mode of arrangement of the soil particles relative to each other and the forces acting between them to hold them in their positions. The conceptis further extended to include the mineralogical composition of the grains, the electrical properties of the particle surface, the physical characteristics, ionic composition of the pore water, the interactions among the solid particles, pore water and the adsorption complex The formation of soil structure is governed by several factors.
In coarse-grained soils, the force of gravity is the main factor, while in fine-grained soils, the surface bonding forces become predominant. The specific surface the ratio of the surface area of a materia! Though this value for soil particles is not computed as they are far too irregular in shape, it is clear that a soil mass made up of many small particles will have a much larger specific surface than the same material made up of large particles.
Another fact which emerges from the concept of specific surface is that for the same void ratio, water contents are more for fine grained soils than for coarse grained soils. Also, the quantity of water needed to just wet the surface of smaller particles in a given volume js Many times more than what is needed in the case of larger particles. Though the clay soils arc fine-grained, not all fine-grained soils possess plasticity and cohesion. The presence of water, which is relatively unimportant in coarse-grained soils, plays a decisive role in the engineering behaviour of aclay soil.
Clay minerals are very active electrochemically and the presence of even a small amount of clay minerals can appreciably alter the engineering properties of a soil mass. Generally, when over 50 per cent of the soil deposit consists of particles whose diameter is 0. These clay minerals are evolved mainly from the chemical weathering of certain rock-forming minerals. Chemically, these minerals are hydrous aluminosili- cates with other metallic ions.
Their particles are very small in size, very flaky in shape and thus have considerable surface area. They can only be viewed with an electron microscope. It is observed that more or less similar engineering properties are exhibited by all clay minerals belonging to. Table 4. The basic concepts concerning atomic structure are fairly well known, Atoms unite together to form molecules, and molecules with other molecules o build up the structure of substances.
The forees binding them together are primarily of electrical nature and itis necessary to know about them before the behaviour of the clay particles and of the aggregate of these particles can be discussed. There are wo main groups of atomic bonds, primary—of high energy bonds which hold the atoms together, and secondary—of weak bonds which link molecules. Sail Structure and Clay Minerals 93 Primary Valence Bond is due to a chemical combination of atoms of two elements which lack a complete complement of clectrons in their outermost or valence shells.
One atom joins with another atom by adding some electrons tqits outer shell or by losing them to arrive at astable configuration. The process usually would mean the loss of addition of the fewest number of electrons. The actual number of electrons an atom gains or loses will be dependent on the valency of the element involved. In the formation of a molecule, such as AlzO , there are 2 ions of Al and 3 ion of O because each Al ion has an excess of 3 electrons in its outer shell, while O has a deficit of two electrons in its outer shell.
Alion gives excess electrons to O ion to form a molecule of AlOs. The ionic bonds are very strong and are not normally broken up in engineering practice. These are much weaker than the primary valence bonds, The secondary valence bonds are of two kinds—van der Waals forces and hydrogen bond. Since the force varies inversely as a power of the distance of separation, the force between two non-parallel erystal surfaces is not merely a function of the average distance between them but is also dependent on the orientation of the surfaces with respect to each other.
In some electrically neutral molecules, such as water molecules, the centres of positive and negative polarity do not coincide, and thus the molecules behave like permanent magnets or dipoles, The force of attraction between the oppositely charged ends of such dipoles is one component of the van der Waals forces and is termed the orientation effect Fig. Secondly, the attractive force between permanent dipoles and dipoles induced by these in adjacent originally non-polar motecules is termed induction effect, and thirdly, the interaction between instantaneous, fluctuating ipoles due to the constant oscillation of the electrons is termed dispersion effect.
The contributions of these effects to the van der Waals forces are: Orientation 77 per cent, Dispersion 19 per cent and Induction 4 per cent. When this is formed between hydrogen and oxygen, the hydrogen atom with a deficiency of electrons, appears to have a positive charge.
The positively charged hydrogen is capable of attracting an oxygen atom of another molecule, thus forming a hydrogen bond. The linkage between water molecules Fig.
In the water molecule, the electrons of the hydrogen atoms are shared by the oxygen atom. Since the engineering properties of the minerals in a group are roughly the same, an examination of the crystal structure of typical clay minerals in these groups will provide a useful insight into the basic engineering behaviour of the clays themselves.
The flakes or platelets of a clay soil consist of many crystal sheets which have a repeating atomic structure. The atomic structures of clay minerals are built of two fundamental crystal sheets, the letrakedral or silica sheet and the octahedral or alumina sheet.
It is only the mode of stacking of these sheets, the nature of bonding forces and the different metallic ions in the crystal lattice that go to make different clay minerals. Tetrahedral Sheer ica tetrahedral units which consist of four oxygen atoms placed at the tips of a tetrahedron enclosing a silicon atom.
Figure 4. The sharing of charges leaves three negative charges at the base per tetrahedral unit. This, along with the two negative charges at the apex, makes a total of five negative charges to four positive charges of the silicon ion.
Thus, there is a net charge of — per unit. A symbolic representation of the silica sheet is shown in Fig. A top view of the silica sheet, shown in Fig. Octahedral Sheet The octahedral sheet is a combination of octahedral units. An octahedral unit has six hydroxy] ions at the tips of an octahedron enclosing an aluminium or magnesium or some other metallic atom. Soil Structure and Clay Minerals 99 Typical Typical Specific thickness diameter surface Edge view a nm loi feg Montmorillonite 3 08 ——— 0 0.
The third reason is that the cations present in water get attracted to the negatively charged surface of the clay particles and water dipoles are, in turn, attracted to the cations. Beyond this, there is an outer layer which is attracted to a lesser degree and is more mobile.
This layer which extends upto the limit of attraction is known a the diffuse-double layer. The three modes of attraction are illustrated in Fig. Also, with the exception of Kaolin, isomorphous substitution, mentioned earlier, is one of the sources of negative charge at the surface of the clay crystal. Positive ions or cations in the water are, therefore, attracted to these surfaces of the particles to render the crystal electrically neutral.
Different clays have different charge deficiencies and have varying ability to adsorb exchangeable cations. The ability of a clay particle to adsorb ions on its surface or edges is called its base or cation exchange capacity which is a function of the mineral structure of the clay and the size of the particles. The base exchange capacity is expressed in terms of the weight of a cation which may be held on the surface of g of dry soil material.
Conventionally, it is measured in millicquivalent meq per of dry soil where 1 meq is 1 mg of hydrogen or the portion of any ion which will combine with or displace 1 mg of hydrogen. On the basis of earlier discussions, it can be seen that montmorillonite has a much greater base exchange capacity than kaolinite, with illite being intermediate in position, as shown in Table 4.
Ca and Mg are the major exchangeable cations in soils. Marine clays have predominantly Na and Mg cations. The valence of the cation is the basic factor in the process of replacement or exchange. Higher valence cations can easily replace lower valence cations.
When the ions have the same valence, larger the size of the ion, greater its replacement capacity. Potassium ion, even though monovalent, has more replacement power than sodium which is also monovalent because of its ability to fit into the hexagonal holes in the silica sheet.
Increased shear strength might be most desirable in some others. It is not possible to have a compacted soil having all desirable properties to an ideal extent. But by choosing a compaction water content slightly dry or slightly wet of optimum, it may be possible to secure an improvement in a set of soil properties which are critical for the performance of that particular project.
Selecting compaction conditions is indeed a problem of optimisation. Table 5. Since the control in the field connot be as strict as in the laboratory, the specifications usually require attainment of 90 to per cent of dry unit weight attained in the laboratory. A fill is made by compacting successive horizontal layers, It is necessary to control the moisture content of the soil which is to be compacted. Also, the moisture content should be as near the chosen value as possible.
If the soil from the barrow pit is too dry, the deficiency of water in the soil may be made up by sprinkling water and mixing it thoroughly before compacting, whereas if the soil is too wet, it may be excavated in advance and dried. The various types of rollers are: smooth wheel rollers, pneumatic tyred rollers and sheepsfoot rollers. Ramming equipmentean be the impact type, internal combustion type or the pneumatic type. Vibrating unit ean be mounted on.
Vibration may be induced by rotating an unbalanced mass or by a pulsating hydraulic system. The compaction achieved in the field would depend on i thickness of lift layer ii type of roller, iti number of passes of the roller, and iv intensity of pressure on the soil.
Application of vibrations is the most effective method of compacting cohesionless soils. Best results are obtained when the frequency of vibrationsis close tothe natural frequency of the soil. The vibrating equipment can be the dropping weight or the pulsating hydraulic type.
In order of effectiveness, watering is the next method that can be used for compacting cohesionless deposits. However, large quantities of water are required in this method. Rolling is the least effective method of compacting cohesicnless soil deposit. Existing loose sand deposits, if subjected to vibrations, also get densified and exhibit less settlement. It is always desirable to compact such deposits by vibroflotation before placing stractures an them, Pile driving.
Compaction of Moderately Cohesive Solls When compacting moderately cohesive soils, best results are obtained when the soils are compacted in layers. These soils are compacted by rollers. Depending upon the plasticity of the soil, pneumatic tyred rollers or sheepsfoot rollers can be used. In the case of silts of low plasticity, pncumatic tyred rollers are preferred. A common form of pneumatic tyred roller consists of a box or platform mounted between two axles, The rear axle has one whee!
The wheel mounted on the front axle is arranged to track in between those mounted on the rear axle, The pneumatic or rubber tyred roller has about 80 per cent coverage, i. The tyre pressures in small rollers are of the order of kPa whercas in heavier rollers.
The soils are usually compacted in about mm thick layers with 8 10 10 passes of the raller, Sheepsfoot rollers are more suitable for plastic soils of moderate plasticity. This type of roller has many round or rectangular shaped projections or feet attached to a steel drum. There is approxi- mately one foot for about 50 to sq em of the surface area of the drum of the ralter. The feet project by about to mm from the drum surface. The weight of the drum can be varied by filling it partly or fully with water or sand.
As the coverage is about 8 to 12 per cent, very high contact pressures, ranging from 1, to 7, kPa, depending upon the drum size and whether the drum is partly or fully filled, are possible.
The sheepsfoot roller starts compacting the soil below the bottom of the foot and works its way up the layer as the passes increase in number. Sheepsfoot rollers are usually towed in tandem by crawler-tractors or are self-propelled, Sheepsfoot rollers induce shear strains in a plastic soil more than any other type of roller, Compaction of Clays When excavated from the borrow pits, clay comes out in the form of chunks.
In case these are required for small scale work. However, for large scale work, it is not economically feasible to get these lumps broken. Further, once the clay has been excavated. All that can be achieved is a reduction in the space between adjacent chunks.
This is satisfactorily achieved by sheepsfoot rollers. Suitability of Compaction Equipment Table 5. Compaction wa libration Penetration resistance in proctor needie Fig. As a number of tests can be conducted by nuclear methods, a better statistical control of the fills is provided. However, the disadvantage of the nuclear method is the relatively high initial cost of the testing equipment and the potential danger to the field personnel from radiation, EXAMPLES Example 5.
IS heavy compaction test uses 4. Example 5. The rammer used for compaction has the foot of area 0. The energy developed per drop of the rammer is 40 kg m. Soil Compaction Solution: In the Indian Standard light compaction test, a cylindrical mould of volume 1, ce is used, The wet unit weight can be obtained by dividing the weight of wet sample by the volume of the mould.
As the water content is known, the dry unit weight can be found by the equation. Hence ha Ye 6. The soil pores ean be visualised as an interconnected but intricate network of irregular tubes. Under equilibrium condition, water level in these tubes rises to the same clevation. This level can be casily determined by inserting a stand-pipe at the point in question and observing the height upto which the water rises in the stand pipe [A in Fig.
Thus the pore water pressure, like the total stress, is also a measurable parameter, A standpipe or a piezometer is used to measure the pore water pressure. Conibining Eqs. The tetfm hy Yy occurs in both Eqs. It is only necessary to make ratio the same for all the fields.
Many of the fields in a flow net are, in fact, far from resembling real squares, but they stil! It is quite clear that no two flow lines can ever meet.
If they did, it would imply that the water flowing in the flow path between them has disappeared, which is a physical impossibility. The equipotential lines cannot meet either, because this would mean that where they meet, there are two potentials in the pore water, which again is an absurdity.
From Eq, 7. The graphical solution of the Laplace's equation, namely the flow net, enables us to determine ny and ry and, thus, the shape factor, which is a function only of the boundary conditions that govern a given flow problem. The flow net would not change, for example.
In each ease, the quantity of seepage would surely be different. Even if the upstream and downstream water levels were to be reversed, the flow net would be the same but the direction of flow would be reversed. It is only when the geometry of the flow space boundary conditions is altered that the flaw net would be different and would yield a ferent — ratio, For a given set of boundary ne conditions, the flow net would be unique.
Uplift pressure Another important use of the flow nets is in calculating uplift pressures under masonry dams. From the flaw net, one can determine the pressure head at any point at the base of the dam, Uplift pressure at any given point is the pore water pressure acting vertically upward due to the residual pressure head at that point. The diagram of distribution of uplift pressure along the base of the dam can be drawn and the total uplift force then calculated by working out the area of the uplift pressure distribution diagram.
Uplift force isan important consideration in the stability of a masonry dam. The total uplift force acts opposite the force of gravity due to the weight of the dam and hence reduces the stability of the hydraulic structure, Uplift pressure computation is illustrated in Example 7. Uplift pressures along the base of masonry dams can be effectively reduced by providing vertical cut off walls at the upstream end of the base of the dam.
Piping may work its way backwards along the base of the dam or along a bedding plane in the soil strata where the resistance is minimum. If piping is not halted, it may result in a catastrophic collapse of the structure.
In fact, a factor of safetly of atleast 6 is recommended for safety against piping. Exit gradient can be reduced to a considerable extent by providing vertical cut off walls at the downstream end of the base of the dam. The calculation of the factor of safety with respect to piping by heave is illustrated in Ex. The factor of safety can be increased by placing a graded filter over the soil prism which is affected. To determine the pressure head 2 point, say A, we select an equipotential line on the flow net passing through that point.
This method is discussed in detail and the other methods are discussed only briefly. It is therefore, not of much practical significance The electrical analogy method is quite extensively used.
The electrical analogy method is based on the fact that the Darcy's law, which govems the flow of water through soils, is analogous to the Ohm's law governing the flow of electricity in a conducting medium.
In the analogy, the current being proportional o the voltage drop is similar to seepage being proportional to head dissipated. Thus, if an clectrical model is constructed such that its boundary conditions are similar to the boundary conditions governing seepage.. The boundary equipotentials are created by using copper strips and for the boundary flow lines, non-conducting strips of ebonite or perspex.
To determine the potential distribution in the electrolyte, the potentiometer connected to a probe through a null indicator system, When the probing-poi the water tray and the contact-point in the potentiometer are at the same potential, balance is obtained and indicated as such in the null indictator.
Using this technique, points corresponding to a certain constant potential can be located by the probe, thus tracing an equipotential line. Several equipotential lines of the flow net may, thus, be traced and the flow net completed by drawing flaw lines to conform to the specific boundary conditions. Alternatively, direct determination of flow lines can be made by interchanging the copper strips and the insulating strips. The equipotentials obtained in this manner are the flow lines for the original boundary conditions.
The electrical analogy method has the disadvantage that the top flow line in an unconfined flow condition can only be located by trial. Capittary flow between two closely spaced parallel glass plates is analogous to two-dimensional flow through soils, A model of the hydraulic structure such as an earth dam, is placed between two glass plates which connect two small tanks. The distance between the plates has to be constant so that the capillary space is of constant width.
When the boundary conditions of the model are the same as those for the seepage problems, flow lines can be traced visually by introducing a dye at different points on the upstream face of the model.
Sand models constructed in water tanks also give a visual demonstration of flow, like the capillary flow models. The water tanks consist of perspex or glass Flumes closed at both ends and have the arrangement to maintain the required water levels at the upsteeam and downstream sides of the model.
If necessary, different materials having ferent K values can be used in the model to simulate field conditions, Flow lines can be traced, as in the capillary analogy method, by injecting dye at different points on the upstream face.
Piezometers are sometimes inserted at various points in the model to measure pressure heads. The graphical methad is most extensively used. The procedure is discussed here in detail.
For the two-dimensional steady flow problem, the flow section is firstdrawn toaconvenientscale, The first step before starting to sketch a flow net is to identify the boundary conditions.
For the problem illustrated in Fig. Thus, AEC is a flow line. FG is a flow line, since water must flow along the impermeable surface and cannot penetrate the impermeable layer.
The pore pressure parameter B expresses the increase in pore pressure, in undrained loading, due to the increase in cell pressure which is a hydrostatic pressure.
B varies from 0 to 1 depending on the degree of saturation S. The relationship between S and B is not linear. Hence, while evaluating A from A. Parameter B can be determined in a UW test. For a completely Saturated sotl,. For a given soil, A depends upon the strain, anisotropy, sample disturbance and the over- consolidation ratio. Table Range of Ay Values for Various S Tipe of soil Ay Very loose, fine saturated sands Highly sensitive to quick clays Normally consolidated clays Lightly overconsolidated clays Heavily preconsolidated elays 0.
Construction of an earthembankment over a softelay deposit, is an example of such a problem. If the rate of construction of the embankment is such sthat pore water pressure in the foundation soil cannot dissipate, undrained loading condition will prevail. The curve is a nonlinear one.
Tangent modulus is the slope of the stress-strain curve, and varies from point to point. The use of initial tangent modulus, which is. Since the shearing resistance builds up in directions towards the wall, the earth pressure gradually increases, If this force reaches a value which the backfill cannot withstand, failure again ensues and slip surfaces develop. The Pressure reaches a maximum value represented by point C Fig. A small increase in stress at this stage will cause a continuous increase in the corresponding strain —a condition known as plastic flow.
Both the conditions find the soil mass in a state of incipient failure. If the soil mass is considered to be a semi-infinite, homogeneous, elastic and isotropic material, it is possible to evaluate the lateral pressure using the theory of elasticity, since there are no displacements at all. The lateral pressure distribution diagram described by Eq. The total pressure P, per unit length of a retaining wall of height H Fig. Hence, the theoretical value may vary widely from the real value.
Therefore, more reliance is placed on the values of K, obtained empirically on the basis of field measurements. Rankine's theory came later but is simpler. It will be discussed first. When plastic equilibrium conditions are realized in limited zones of soil, they are known as the local states of plastic equilibrium.
The development of earth pressure against a retaining wall is a consequence of a portion of the backfill coming under plastic equilibrium condition. Rankine considered a semi-infinite mass of soil bound by a horizonial surface and a vertical boundary formed by the vertical back of a smooth wall surface, as shown in Fig. The soil mass is assumed to be homogeneous, dry and cohesionless.
The theory has, however, been extended to include cohesive soils and submerged soils too. The two sets of failure planes are shown in Fig. On the other hand, if the wall moves towards the backfill, there will be a uniform compression in the horizontal direction. This leads to an increase in the value of o, from its original value, while the value of o- remains constant. The soil is then said to be:in the passive Rankine state and the corresponding lateral siress is called the passive earth pressure, p,.
Ttean be seen from Fig. The backfill soil is isotropic, homogeneous and is cohesionless. The soil is in a state of plastic equilibrium during active and passive earth pressure conditions. The rupture surface is a planar surface which is obtained by considering the plastic equilibrium of the soil 4.
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