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PANDIAN SARASWATHI YADAV ENGINEERING COLLEGE
DEPARTMENT OF CIVIL ENGINEERING
CE 6405 SOIL MECHANICS
Prepared by R.Devananth., M.Tech AP/CIVIL
UNIT I –SOIL CLASSIFICATION AND COMPACTION
PART A (TWO MARKS QUESTIONS WITH ANSWERS)
1. Define Soil Mechanics.
The branch of science concerned with the properties and behaviour of soil as they affect its use in civil engineering. Or the branch of mechanics that deals with the action of forces on soil masses is called soil mechanics.
2. Draw the phase diagram of soil.
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3. Distinguish between Residual and Transported soil. Residual soil:
A soil formed by the weathering of the bedrock immediately beneath it.A residual soil is formed 'in place'. It is made up of rock particles weathered from the bedrock below and it is therefore chemically similar to that bedrock. It will also contain organic material derived from plants and animals living in the area.
Transported soil:
A soil that has been transported (eroded) and then deposited in a region where it was not originally formed.Transported soils are the result of erosion and deposition by wind, water, and ice. Transported soils may have properties very different from the bedrock beneath them since they are unrelated. Most soils are transported. This is because the forces of erosion and deposition are constantly at work.
4. Give the relation between γsat, G, γw and e.
γsat= (G+e) γw /(1+e)
5. A compacted sample of soil with a bulk unit weight of 19.62 kN/m3 has a water content of 15 per cent. What are its dry unit weight, degree of saturation and air content? Assume G = 2.65.
Solution:
γd= γ /1+w = 19.62 / 1+0.15 = 17.06 kN/m3 e = G γw/ γd-1= 2.65 x 9.81 / 17.06 – 1 = 0.52
Sr = wG /e = 0.15 x 2.65 / 0.52 = 0.76 x 100=76% ac= 1-Sr = 1-0.76 = 0.24 x 100 = 24%
6. What is porosity of a given soil sample?
A ratio, usually expressed as a percentage, of the volume of voids in a soil to the total volume of the soil, including the voids. The voids permit gases or liquids to pass through the material. n
=Vv / V x 100
7. What is water content in given mass of soil?
The ratio of the mass of water present to the mass of solid particles is called the water content (w), or sometimes the moisture content.
8. Define effective size of particle in sieve analysis.
D10 is termed as the effective particle size it means that 10 percent of the particles are finer and
90 percent of the particles are coarser than that particular particle size D10.
9. List any one expression for finding dry density of soils.
ρd=ρ / 1+w
10. Define unit weight of soil.
The bulk unit weight is simply defined as the weight per unit volume.
_
γbulk
= _
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11. What are all the Atterberg limits for soil and why it is necessary? Atterberg limits:
The Atterberg limits are a basic measure of the critical water contents of a fine-grained soil, such as its shrinkage limit, plastic limit, and liquid limit. As a dry, clayey soil takes on increasing amounts of water, it undergoes dramatic and distinct changes in behavior and consistency. Depending on the water content of the soil, it may appear in four states: solid, semi-solid, plastic and liquid. In each state, the consistency and behavior of a soil is different and consequently so are its engineering properties.Thus, the boundary between each state can be defined based on a change in the soil's behavior. The Atterberg limits can be used to distinguish between silt and clay, and it can distinguish between different types of silts and clays. These limits were created by Albert Atterberg, a Swedish chemist. They were later refined by Arthur Casagrande.
Necessity:
These distinctions in soil are used in assessing the soils that are to have structures built on. Soils when wet retain water and some expand in volume. The amount of expansion is related to the ability of the soil to take in water and its structural make-up (the type of atoms present). These tests are mainly used on clayey or silty soils since these are the soils that expand and shrink due to moisture content. Clays and silts react with the water and thus change sizes and have varying shear strengths. Thus these tests are used widely in the preliminary stages of designing any structure to ensure that the soil will have the correct amount of shear strength and not too much change in volume as it expands and shrinks with different moisture contents.
12. Determine the maximum possible voids ratio for a uniformly graded sand of perfectly spherical grains.
Solution:
The soil will have maximum possible voids when its grains are arranged in a cubical array of spheres. Consider a unit cube of soil having spherical particles of diameter d. Volume of each
spherical particle = / 6 x d3.
Total volume of container = 1 x 1 x 1 = 1
No. of solids in the container = 1/d x 1/d x 1/d = 1/d3. Volume of solids Vs = [ / 6 x d3] x [1/d3] = = / 6
Volume of voids Vv = 1- / 6
Void ratio, e = = 1 - / 6 / / 6 = 0.9099. Porosity, n =e / 1+e = 0.9099 / (1+0.9099) =0.4767. n = 0.4767 x 100 = 47%.
13. Define :(a) Porosity (b) Void ratio. Porosity:
A ratio, usually expressed as a percentage, of the volume of voids in a material to the total volume of the material, including the voids. The voids permit gases or liquids to pass through the material.
Void ratio:
In a soil mass, or the like, the ratio of the volume of the void space to the volume of the solid particles.
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14. Define degree of saturation.
The ratio of the volume of water in a given soil mass to the total volume of intergranular space, expressed as a percentage.
Write any two engineering classification system of soil.
Particle size classification
Textural classification
Highway Research Board (HRB) classification
Unified soil classification and IS classification
Define sieve analysis and sedimentation analysis and what is the necessity of these two analyses?
Sieve Analysis
A sieve analysis (or gradation test) is a practice or procedure used (commonly used in civil engineering) to assess the particle size distribution (also called gradation) of a granular material.
Sedimentation Analysis:
Sedimentation analysis is used only for the soil fraction finer than 75 microns. Soil particles are allowed to settle from a suspension. The decreasing density of the suspension is measured at various time intervals. The procedure is based on the principle that in a suspension, the terminal velocity of a spherical particle is governed by the diameter of the particle and the properties of the suspension.
In this method, the soil is placed as a suspension in a jar filled with distilled water to which a deflocculating agent is added. The soil particles are then allowed to settle down. The concentration of particles remaining in the suspension at a particular level can be determined by using a hydrometer. Specific gravity readings of the solution at that same level at different time intervals provide information about the size of particles that have settled down and the mass of soil remaining in solution. The results are then plotted between % finer (passing) and log size.
Necessity:
Sieve analysis has, in general, been used for decades to monitor material quality based on particle size. For coarse material, sizes that range down to #100 mesh (150μm), a sieve analysis and particle size distribution is accurate and consistent.
Sedimentation analysis is used to find out the percentage of silt and percentage of clay.
17. Twoclays A and B have the following properties:
Atterberg limits
Clay A
Clay B
Liquid limit
44%
55%
Plastic limit
29%
35%
Natural water content
30%
50%
Which of the clays A or B would experience more plasticity?
Solution:
Plasticity Index for soil A = 44-29 = 15
Plasticity Index for soil B = 55-35 = 20.
Since Plasticity index of soil B is greater, soil B is more plasticthan soil A.
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18. What is a zero air voids line? Draw a compaction curve and show the zero air voids line.
The compaction curve is a plot of dry unit weight versus water content resulting from a laboratory test in which a soil is compacted in to a mould with a certain amount of compactive effort. The zero air void line is a limiting line corresponding to there being no air in the soil i.e. it is saturated with water.
19. What are the laboratory methods of determination of water content?
Oven drying method
Sand bath method
Alcohol method
Calcium Carbide method
Pycnometer method
Radiation method
Torsion balance method.
Define specific gravity and density index.
Specific gravity:
Ratio of the weight of a given volume of a substance to the weight of an equal volume of some reference substance, or, equivalently, the ratio of the masses of equal volumes of the two substances.
Density Index:
Relative density or density index is the ratio of the difference between the void ratios of a cohesionless soil in its loosest state and existing natural state to the difference between its void ratio in the loosest and densest states.
What do understand from grain size distribution?
In soil mechanics, it is virtually always useful to quantify the size of thegrains in a type of soil. Since a given soil will often be made up of grainsof many different sizes, sizes are measured in terms of grain size distributions.
Grain size distribution (GSD) information can be of value in providing initial rough estimates of a soil’s engineering properties such as permeability, strength, expansivity, etc.
22. What are the various types of gradations of soil?
The process of grading a soil is in accordance with either the Unified Soil Classification System or the AASHTO Soil Classification System. The steps in grading a soil are data collection, calculating coefficients of uniformity and curvature, and grading the soil based on the grading criteria given in the used soil classification system.
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23. Classify the soil based on particle size as per Indian Standards.
Coarse grained soils
Boulder
Cobble
Gravel (G) iv)Sand (S)
Fine grained soils
Silt (M)
Clay (C)
Organic matter (O)
c) Highly organic soils and other miscellaneous soil materials.
Fibrous organic matter (eg. Peat and decomposed vegetation)
Shells
Concretions
Cinders
24. What do you understand from uniformly graded soil?
A poorly graded soil is a soil that does not have a good representation of all sizes of particles from the No. 4 to No. 200 sieve. Poorly graded gravel is classified as GP while poorly graded sand is classified as SP. Poorly graded soils are more susceptible to soil liquefaction than well graded soils. A soil having particles of nearly the same size is known as poorly graded soil.
25. What are consistency limits of soil?
The Atterberg limits are a basic measure of the critical water contents of a fine-grained soil, such as its shrinkage limit, plastic limit, and liquid limit. As a dry, clayey soil takes on increasing amounts of water, it undergoes dramatic and distinct changes in behavior and consistency.
26. Define flow index.
The flow index (If), which is the slope of the water content versus log10 (number of blows) plot
in the percussion cup method or the slope of the water content versus log10 (depth of penetration) plot of the cone penetration method of determining the liquid limit of soils is a measure of soil plasticity. Hence, the plasticity index of a soil that represents the soil plasticity can be correlated with the flow index.
What are the methods available for determination of in-situ density? i) Sand replacement method
ii) Core cutter method
iii) Water displacement method iv) Rubber balloon method.
What is shrinkage ratio?
The ratio of a volume change to the moisture-content change above the shrinkage limit.
29. What is the function of A-line Chart in soil classification?
The A-line generally separates the more clay like materials from those that are silty and also the organic soils from inorganic soils.
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Define plasticity index and liquidity index. Plasticity Index:
The plasticity index (PI) is a measure of the plasticity of a soil. The plasticity index is the size of the range of water contents where the soil exhibits plastic properties. The PI is the difference between the liquid limit and the plastic limit (PI = LL-PL).
Liquidity index:
The liquidity index (LI) is used for scaling the natural water content of a soil sample to the limits. It can be calculated as a ratio of difference between natural water content, plastic limit, and liquid limit: LI= (W-PL)/ (LL-PL) where W is the natural water content.
Define consistency and toughness index.
Consistency index:
The consistency index or the relative consistency is defined as the ratio of the liquid limit minus the natural water content to the plasticity index of a soil.
Toughness index:
The ratio between the index of plasticity and the flow index of a soil.
Write the major soil classifications for general engineering purposes. i) Particle size classification
ii) Textural Classification
iii) Highway Research Board (HRB) classification
iv) Unified soil classification and IS classification system.
Define compaction.
In geotechnical engineering, soil compaction is the process in which a stress applied to a soil causes densification as air is displaced from the pores between the soil grains.
34. Differentiate standard proctor from modified proctor test.
S.No.
Standard Proctor Compaction Test
Modified Proctor Compaction Test
1.
The standard Proctor test was developed
The modified Proctor test was developed to
to give a lighter standard of compaction.
give a higher standard of compaction.
Soil compacted in three layers and 25
Soil compacted in five layers and 25 blows
2.
blows for 1000ml is given.
for 1000ml and 55 blows for 2250 ml are
given.
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UNIT I - PART B (QUESTIONS)
1. Write down a neat procedure for determining water content and specific gravity of a given soil in the laboratory by using a pycnometer.
2.Sandy soil in a borrow pit has unit weight of solids as 25.8 kN/m3, water content equal to 11%
and bulk unit weight equal to 16.4 kN/m3. How many cubic meter of compacted fill could be
constructed of 3500 m3 of sand excavated from borrow pit, if required value of porosity in the compacted fill is 30%. Also calculate the change in degree of saturation.
3. The following data on consistency limits are available for two soils A and B.
SI.NO.
Index
Soil A
Soil B
1
Plastic limit
16%
19%
2
Liquid limit
30%
52%
3
Flow index
11
06
4
Natural water content
32%
40%
Find which soil is
More plastic.
Better foundation material on remoulding.
Better shear strength as function of water content.
Better shear strength at plastic limit.
Classify the soil as per IS classification system. Do those soils have organic matter?
4.By three phase soil system, prove that the degree of saturation S (as ratio) in terms of mass unit
weight (γ), void ratio (e), specific gravity of soil grains (G) and unit weight of water (γw) is given
by the expression
5. The mass of wet soil when compacted in a mould was 19.55 kN. The water content of the soil
was 16%. If the volume of the mould was 0.95 m3. Determine (i) dry unit weight, (ii) Void ratio,
(iii) degree of saturation and (iv) percent air voids. Take G = 2.68.
6.A soil sample has a porosity of 40 per cent. The specific gravity of solids is 2.70. calculate i)
Voids ratio ii) Dry density and iii) Unit weight if the soil is completely saturated.
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7. In a hydrometer analysis, the corrected hydrometer reading in a 1000 ml uniform soil suspension at the start of sedimentation was 28. After a lapse of 30 minutes, the corrected hydrometer reading was 12 and the corresponding effective depth 10.5 cm. the specific gravity of the solids was 2.68. Assuming the viscosity and unit weight of water at the temperature of the
test as 0.001 Ns/m2 and 9.81 kN/m3 respectively. Determine the weight of solids mixed in the suspension, the effective diameter corresponding to the 30 minutes reading and the percentage of particle finer than this size.
8.An earthen embankment of 106 m3 volume is to be constructed with a soil having a void ratio of 0.80 after compaction. There are three borrow pits marked A, B and C having soils with voids ratios of 0.90, 0.50 and 1.80 respectively. The cost of excavation and transporting the soil is Rs
0.25, Rs 0.23 and Rs 0.18 per m3 respectively. Calculate the volume of soil to be excavated from each pit. Which borrow pit is the most economical? (Take G = 2.65).
9.A laboratory compaction test on soil having specific gravity equal to 2.67 gave a maximum dry
unit weight of 17.8 kN/m3 and a water content of 15%. Determine the degree of saturation, air content and percentage air voids at the maximum dry unit weight. What would be theoretical maximum dry unit weight corresponding to zero air voids at the optimum water content?
10. A soil has a bulk unit weight of 20.11 KN/m3 and water content of 15 percent. Calculate the
water content of the soil partially dries to a unit weight of 19.42 kN/m3 and the voids ratio remains unchanged.
11.Explain Standard Proctor Compaction test with neat sketches.
12.Explain all the consistency limits and indices.
Explain in detail the procedure for determination of grain size distribution of soil by sieve analysis.
An earth embankment is compacted at a water content of 18% to a bulk density of 1.92 g/cm3. If the specific gravity of the sand is 2.7, find the void ratio and degree of saturation of the compacted embankment.
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15. Soil is to be excavated from a barrow pit which has a density of 17.66kN/m3 and water content of 12%. The specific gravity of soil particle is 2.7. The soil is compacted so that water
content is 18% and dry density is16.2 kN/m3. For 1000 cum of soil in fill, estimate.
The quantity of soil to be excavated from the pit in cum and
The amount of water to be added. Also determine the void ratios of the soil in borrow pit and
fill.
16.Explain the procedure for determining the relationship between dry density and moisture
content by proctor compaction test.
Explain in detail the Indian standards classification system.
Describe in detail the procedure for determination of liquid limit of soil
Describe in detail the procedure for determination of shrinkage limit of soil
Explain in detail the factors affecting compaction.
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UNIT II –SOIL WATER AND WATER FLOW
PART A (TWO MARKS QUESTIONS WITH ANSWERS)
1. Define soil water.
Water present in the voids of soil mass is called soil water.
2. Classify the types of soil water.
Broad classification
Free water or gravitational water
Held water
Structural water
Adsorbed water
Capillary water
Classification on phenomenological basis
Ground water
Capillary water
Adsorbed water
Infiltered water
Classification on structural aspect
Pore water
Solvate water
Adsorbed water
Structural water
3. Define Capillarity.
The tendency of a liquid in a capillary tube or absorbent material to rise or fall as a result of surface tension.
4. What is surface tension?
The tension of the surface film of a liquid caused by the attraction of the particles in the surface layer by the bulk of the liquid, which tends to minimize surface area.
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5. What is meant by capillary s iphoning?
Capillary forces can raise the water in the capillary tube against force of gravity. Some phenomenon takes place in the voids of dry soil. In case of earth dams, this may create serious problems. If the top of the core is situated at a height y, hc (critical height) above the H.F.L. (High Flood Level) the capillar y forces will pull the water in the descending part of the earth dam, and will slowly empty it. The process, known as capillary siphoning, m ay continue for a very long duration.
6. Briefly explain the concept o f effective stress.
Effective stress is a force that k eeps a collection of particles rigid. Usually thi s applies to sand, soil, or gravel.
Karl von Terzaghi first propose d the relationship for effective stress in 1925.F or him, the term "effective" meant the calculated stress that was effective in moving soil, or causing displacements. It represents the a verage stress carried by the soil skeleton.
Effective stress (σ') acting on a soil is calculated from two parameters, total stress (σ) and pore water pressure (u) according to:
7. What is neutral stress?
The neutral stress or the pore wa ter pressure or pore pressure is the pressure or stress transmitted through the pore fluid. This pres sure or stress, equal to water load per unit area above the plane, does not have any measurable i nfluence on the voids ratio or any other mechanical property of the soil, such as the shearing resi stance.
Give the relationship betwee n total, neutral and effective stress.
Define permeability.
Soil permeability is the property of the soil to transmit water and air through its interconnecting voids spaces.Permeability is th e measure of the soil’sability to permit water to flow through itspores or voids.
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What are the factors affecting permeability?
Particle size
Structure of soil mass
Shape of particles
Void ratio
Properties of water
Degree of saturation
Adsorbed water
Impurities in water.
What are the methods available for determination of permeability in the laboratory?
Constant head permeability test
Falling head permeability test.
What is Darcy’s Law?
Darcy's law is a phenomenologically derived constitutive equation that describes the flow of a fluid through a porous medium. The law was formulated by Henry Darcy based on the results of experimentson the flow of water through beds of sand. It also forms the scientific basis of fluid permeability used in the earth sciences, particularly in hydrogeology. Mathematically, q=k i A.
13. Define discharge and seepage velocity.
Discharge Velocity is obtained by Dividing the Total Discharge by the total cross Sectional Area, Where Total cross sectional area Consists of void+solid. In contrast, Seepage Velocity is defined as the total discharge by the Area of voids only. So Seepage velocity always greater than Discharge Velocity.
Discharge velocity:
Discharge velocity is the quantity of flow that flows through a unit cross sectional area of the soil in a unit time discharge velocity is used to determine the quantity of flow through soil.
Seepage velocity:
The actual rate of movement of the water as measured with dye tracer for instance is the seepage velocity.
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What are methods of determination of permeability in the field?
Pumping-out test.
Pumping-in test.
Define seepage pressure.
By virtue of the viscous friction exerted on water flowing through soil pores, an energy transfer is affected between the water and the soil. The force corresponding to this energy transfer is called the seepage force or seepage pressure.
16. What is quick sand condition?How would you calculate the hydraulic gradient required
to create quick sand conditions in a sample of sand?
The quick condition of soil is the condition when the upward water pressure gradient and water flow reduce the effective stress, i.e., cohesiveness of the soil. Sandy soils may lose their shear strength, and the soil may behave as a fluid. Cohesive soils may produce cracks with water seepage.
ic = γ’/ γw = (G-1) / (1+e)
17. Define Flow net.
A flownet is a graphical representation of two-dimensional steady-state groundwater flow through aquifers.
Construction of a flownet is often used for solving groundwater flow problems where the geometry makes analytical solutions impractical. The method is often used in civil engineering, hydrogeology or soil mechanics as a first check for problems of flow under hydraulic structures like dams or sheet pile walls. As such, a grid obtained by drawing a series of equipotential lines is called a flownet. The flownet is an important tool in analysing two-dimensional irrotational flow problems.
18. Define flow line and equipotential lines.
Flow Lines are the paths which water particle follow in the course of seepage. Water flows from the point of higher head to low head.
Equipotential lines are the lines formed by joining the points of same head or potential on the flow lines.
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19. Define velocity potential and stream function.
A velocity potential is a scalar potential used in potential flow theory. It was introduced by Joseph-Louis Lagrange in 1788.It is used in fluid dynamics, when a fluid occupies a simply-connected region and is irrotational.
The stream function is defined for incompressible (divergence-free) flows in two dimensions – as well as in three dimensions with axisymmetry. The flow velocity components can then be expressed as the derivatives of the scalar stream function.
20. What are the applications of flow net?
Determination of seepage: For the seepage through a flow net for isotropic condition.Total
Discharge, q = k.h.Nf/Nd, where, k = co-efficient of permeability, h= head causing flow, Nf=
Total numbers of flow channels&Nd= Total numbers of potential drops.
Determination of seepage pressure: The change in the effective pressure due to flow of water is
known as seepage pressure. The seepage pressure at any point can be determined byPs= H.Yw,
where, H= hydraulic potential at any point, Yw = h - n.h/Nd = (Nd-n).h/Nd , n = numbers of
potential drops.
Hydrostatic pressure at a point
Exit gradient.
What are the properties of flow nets?
Flow lines and equal potential lines intersect each other at 90 degrees.
The areas bounded by the flow lines and equal potential lines form approximate squares.
Flow nets must satisfy the boundary conditions of flow field.
Quantity of water flowing through each flow channel is the same.
The potential drop in any two consecutive equal potential lines is same/constant.
Flow lines and equal potential lines are smooth curves.
What is meant by phreatic line?
Phreatic line is a seepage line passing from the water level point up to the provided filter. It is the graphical representation of the seepage line.
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List out the methods of drawing flow net.
Graphical method.
Electrical analogy method.
What is meant by total stress, neutral stress and effective stress? Total Pressure/stress:
The total vertical stress acting at a point below the ground surface is due to the weight of everythinglying above: soil, water, and surface loading. Total stresses are calculated from the unit weight of the soil. (σ = σ' +u)
Pore water pressure / neutral stress:
The water in the pores of a soil is called porewater. The pressure within this porewater is called pore pressure (u). The magnitude of pore pressure depends on: (i) the depth below the water table (ii) the conditions of seepage flow. The neutral stress or the pore water pressure or pore pressure is the pressure or stress transmitted through the pore fluid. This pressure or stress, equal to water load per unit area above the plane, does not have any measurable influence on the voids ratio or any other mechanical property of the soil, such as the shearing resistance.
Effective stress:
The difference between the total stress and the pore pressure is called the effective stress:
σ' = σ -u
Karl von Terzaghi first proposed the relationship for effective stress in 1925.For him, the term "effective" meant the calculated stress that was effective in moving soil, or causing displacements. It represents the average stress carried by the soil skeleton.
25. What is meant by capillary rise in soil and how it affects the stress level in soils?
Capillary action (sometimes capillarity, capillary motion, or wicking) is the ability of a liquid to flow in narrow spaces without the assistance of, and in opposition to, external forces like gravity.Above the water table up to the height of capillary rise is the capillary zone and the water is called capillary water. The water pressure is negative (less than atmospheric) in the capillary zone.
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26. For a homogeneous earth dam 52 m high and 2 m free board, a flow net was constructed and following results were obtained: Number of potential drops = 25; Number of flow channels = 4. Calculate the discharge per metre length of the dam if the co-efficient
of permeability of the dam material is 3 x 10-5 m/sec.
Solution:
The discharge per unit length is given by q = kHNf / Nd
Here H = water depth = 52-2=50m. K = 3 x 10 -5 cm /sec. Nf= 4. Nd = 25.
q = 3 x 10 -5 cm /sec x 50m x 4 /25 = 24 x 10 -5 m3/sec/m. = 0.00024 cumecs/metre length.
27. Write down the uses of Flow net.
To determine the amount of seepage and upward lift pressure below hydraulic structure.Once the flow net is constructed, the same one applies to flows at different discharges.If the velocity of any reference point is known, the flow net gives velocity at any point by using continuity equation. A flow net analysis assists in the design of an efficient boundary shapes.If helps in avoiding the separation and the points of stagnation in the design of boundary shapes.
28. What are methods of determination of permeability in the field?
Pumping –out tests
Pumping –in tests.
29. What are the different methods to determine co-efficient of permeability?
The coefficient of permeability can be determined by the following methods.
(i) Laboratory methods
Constant Head permeability tests
Falling head permeability tests.
(ii) Field methods.
Pumping –out tests.
Pumping-in tests.
(iii) Indirect methods.
Computation from grain size or specific surface.
Horizontal capillarity test
Consolidation test data.
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UNIT II - PART B (QUESTIONS)
1. The water table in a deposit of sand 8 m thick is at a depth of 3 m below the ground surface. Above the water table, the sand is saturated with capillary water. The bulk density of sand is
19.62 kN/m3. Calculate the effective pressure at 1m, 3m and 8m below the ground surface. Hence plot the variation of total pressure, neutral pressure and effective pressure over the depth of 8m.
2.Write down the procedure for determination of permeability by constant head test in the laboratory.
Compute the total, effective and pore pressure at a depth of 20 m below the bottom of a lake 6 m deep. The bottom of lake consists of soft clay with a thickness of more than 20 m. the average water content of the clay is 35% and specific gravity of the soil may be assumed to be 2.65.
What will be the ratio of average permeability in horizontal direction to that in the vertical direction for a soil deposit consisting of three horizontal layers, if the thickness and permeability of second layer are twice of those of the first and those of the third layer twice those of second?
The subsoil strata at a site consist of fine sand 1.8 m thick overlying a stratum of clay 1.6 m thick. Under the clay stratum lies a deposit of coarse sand extending to a considerable depth. The water table is 1.5 m below the ground surface. Assuming the top fine sand to be saturated by capillary water, calculate the effective pressures at ground surface and at depths of 1.8 m, 3.4 m and 5.0 m below the ground surface. Assume for fine sand G = 2.65, e = 0.8 and for coarse sand G = 2.66, e = 0.5. What will be the change in effective pressure at depth 3.4 m, if no capillary water is assumed to be present in the fine sand and its bulk unit weight is assumed to be 16.68
kN/m3. The unit weight of clay may be assumed as 19.32 kN/m3.
Explain the falling head permeability test.
What are the applications of flow net and explain briefly?
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8.In a constant head permeameter test, the following observations were taken. Distance between piezometer tappings = 15 cm, difference of water levels in piezometers = 40 cm, diameter of the test sample = 5 cm, quantity of water collected = 500 ml, duration of the test = 900 sec.Determine the coefficient of permeability of the soil. If the dry mass of the 15 cm long sample is 486 g and specific gravity of the solids is 2.65. Calculate seepage velocity of water during the test.
9.A foundation trench is to be excavated in a stratum of stiff clay, 10m thick, underlain by a bed of coarse sand (fig.1.). In a trial borehole the ground water was observed to rise to an elevation of 3.5m below ground surface. Determine the depth upto which an excavation can be safely carried out without the danger of the bottom becoming unstable under the artesian pressure in the sand stratum. The specific gravity of clay particles is 2.75 and the void ratio is 0.8. if excavation is to be carried out safely to a depth of 8m, how much should the water table be lowered in the vicinity of the trench?
10. The following data were recorded in a constant head permeability test. Internal diameter of permeameter = 7.5cm
Head lost over a sample length of 18cm = 24.7cm Quantity of water collected in 60 Sec = 626 ml Porosity of soil sample was 44%
Calculate the coefficient of permeability of the soil. Also determine the d ischarge velocity and seepage velocity during the test.
11. Determine the effective stress at 2m, 4m, 6m, 8m and 10m is a soil mass having γs=21
KN/m3. Water table is 2m below ground surface. Above water table there is capillary rise upto ground surface. Also draw total stress diagram up to 10m.
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12. A stratified soil deposit is shown in Fig. Along with the coefficient of permeability of the individual strata. Determine the ratio of KH and KV. Assuming an average hydraulic gradient of 0.3 in both horizontal and vertical seepage, Find
Discharge value and discharge velocities in each layer for horizontal flow and
Hydraulic gradient and loss in head in each layer for vertical flow.
Explain any four methods of obtaining flow nets.
The discharge of water collected from a constant head permeameter in a period of 15 minutes is 500 ml. the internal diameter of the permeameter is 5 cm and the measured difference in head between two gauging points 15 cm vertically apart is 40 cm. calculate the coefficient of
permeability. If the dry weight of the 15 cm long sample is 486 gm and the specific gravity of the solids is 2.65, calculate the seepage velocity.
Explain in detail the laboratory determination of permeability using constant head method and falling head method.
16.Explain in detail the procedure for drawing the phreatic line for an earthen dam.
Derive the Laplace equation for two-dimensional flow.
Explain in detail the properties and applications of flow nets.
Explain in detail the procedure for drawing the phreatic line for an earthen dam.
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UNIT III - STRESS DISTRIBUTION, COMPRESSIBILITY AND SETTLEMENT
PART A (TWO MARKS QUESTIONS WITH ANSWERS)
1.What are the assumptions of BoussinesqEqutions?
The soil mass is an elastic medium for which the modulus of Elasticity, E is constant.
The soil mass in homogeneous that is all its constituent parts or elements are similar and it has identical properties at every point in it in identical directions.
The soil mass is isotropic, that is it has identical elastic properties in all directions through any point of it.
The soil mass is semi‐infinite, that is it extends infinitely in all directions below a level surface.
Name the vertical stress distribution diagrams drawn using Boussinesq equation?
Vertical stress isobar diagram
Vertical pressure distribution on a horizontal plane.
Vertical pressure distribution on a vertical line.
2. Define normally consolidated clays and over consolidated clays.
Define isobar.
An isobar is a curved or contour connecting all points below the ground surface of equal vertical pressure.
4.Define pressure bulb.
The zone in a loaded soil mass bounded by an isobar of given vertical pressure intensity is called a pressure bulb.
5.Define Influence Value.
In Newmarks influence value a circle is drawn with radius r1 equal to 0.270z and the are is divided into 20 area units, each area unit will produce a vertical stress equal to 0.005q at a depth of z cm below the centre. The arbitrarily fixed fraction 0.005 is called influence value.
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6. Give the formulae to determine the vertical stress, radial stress Tangential stress, & shear stress uner a point load.
7. Give the formulae to determine the vertical stress, horizontal stress under a circular load.
7. Write an equation of vertical pressure in uniformly loaded rectangular area.
8. Explain the method of estimating vertical stress using Newmark’s influence chart.
Newmark’s Influence Chart is an illustration used to determine the vertical pressure at any point below a uniformly loaded flexible area of soil of any shape. This method, like others, was derived by integration of Boussinesq’s equation for a point load.
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Consider a circular area of radius r loaded uniformly by a distributed load of intensity p. The vertical displacement s of a poin t at a distance Z beneath the center of the circ ular area is given by the following formula:
Where,
For the surface of the loaded are a Z = 0 and, consequently, a = r/2.
9. What is the principle of Ter zaghi’s one dimensional consolidation theory ?
Terzaghi's Principle states that when a rock is subjected to a stress, it is opposed by the fluid pressure of pores in the rock. More specifically, Karl von Terzaghi's Princ iple, also known
as Terzaghi's theory of one-dimensional consolidation, states that all qua ntifiable changes
in stress to a soil [compression, deformation, shear resistance] are a direct resu lt of a change in effective stress. The effective stress is related to total stress and the pore p ressure by the relationship;
reading that total stress is equal to the sum of effective stress and pore water pre ssure.
What are the assumptions made in Terzaghi’s one dimensional consolid ation theory?
The soil is homogenous (uniform in composition throughout).
The soil is fully saturated (zero air voids due to water content being so hi gh).
The solid particles and water are incompressible.
Compression and flow are one-dimensional (vertical axis being the one o f interest).
Strains in the soil are rela tively small.
Darcy's Law is valid for all hydraulic gradients.
The coefficient of permeability and the coefficient of volume compressibility remain constant throughout the p rocess.
There is a unique relatio nship, independent of time, between the void r atio and effective stress.
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11. What is the use of influence chart in soil mechanics?
Newmark’s Influence Chart is an illustration used to determine the vertical pressure at any point below a uniformly loaded flexible area of soil of any shape.
12. Differentiate between ‘Compaction’ and ‘Consolidation’.
S.No.
Compaction
Consolidation
1.
Soil is made up of three main elements:
In contrast, consolidation is the act of
solid particles, air voids and water voids.
squeezing the water voids out of the soil.
Compaction is when an element of
While this is relatively easy with coarse soils
outside stress squeezes the air voids from
such as sand, it is an expensive and time-
the soil, decreasing its volume and
consuming process with silts and clays. If
increasing its density. This is often done
the soil being consolidated has never
intentionally, using a method such as a
experienced an equivalent outside stress to
roller or a vibrating instrument. There is
the one being used for consolidation, it is
alsoamethodcalled"dynamic
considered "normally loaded," whereas if it
compaction," which involves dropping a
has, it is considered "pre-consolidated." Pre-
weight on the soil over and over again.
consolidated soil is preferred for purposes of
The degree of compaction depends on
building foundations. Consolidation is often
many different factors: the method used
performed with similar instruments to those
to compact, the amount of water to the
used for compaction, only with drains
amount of air in the soil, the type of soil
installed to wick the water away from the
(silt, clay, sand or something else), and so
soil.
on.
13. What are isochrones?
A line on a diagram or map connecting points relating to the same time or equal times.
14. When a soil mass is said to be homogeneous?
Denoting a process involving substances in the same phase (solid, liquid, or gaseous). A soil mass is said to be homogeneous when upto a depth the nature of the soil is same without any change.
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15. What are isobars?
An isobar is a line which connects all points of equal stress below the ground surface. In other words, an isobar is a stress contour.
List the components of settlement in soil.
Immediate settlement
Consolidation Settlement,
Secondary compression (creep)
What is oedometer?
An oedometer test is a kind of geotechnical investigation performed in geotechnical engineering that measures a soil's consolidation properties. Oedometer tests are performed by applying different loads to a soil sample and measuring the deformation response. The results from these tests are used to predict how a soil in the field will deform in response to a change in effective stress.
18. Define co-efficient of compressibility.
The co-efficient of compressibility is defined as the decrease in voids per unit increase of
pressure.
What are the methods to determine co-efficient of consolidation?
Define over consolidation ratio and creep.
The over consolidation ratio or OCR is defined as the highest stress experienced divided by the current stress. A soil which is currently experiencing its highest stress is said to be normally consolidated and to have an OCR of one.
Downhill creep, also known as soil creep or commonly just creep, is the slow downward progression of rock and soil down a low grade slope; it can also refer to slow deformation of such materials as a result of prolonged pressure and stress.
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21. Write down Boussinesque equation for finding out the vertical stress under a single concentrated load.
σz =
22. Define normally consolidated clays and over consolidated clays. Normally consolidated clays:
If the initial vertical effective stress is approximately equals to the pre-consolidation stress then this condition is known as normally consolidated.”Or “The soil whose present effective overburden pressure is the maximum pressure that the soil was subjected to in the past.”
In real world these two values are subjected to error due to sample disturbance and other factors. That is why the values obtained are rarely equal even if the soil is truly normally consolidated. In order to avoid misclassifying of soil, we will consider that the soil is normally consolidated if initial vertical effective stress and pre-consolidation stress are equal within about 20 percent.
Over consolidated clays:
“If the initial vertical effective stress of the soil sample is less than the pre-consolidation stress, then the vertical effective stress in the field was once higher than its current magnitude, and the soil is called overconsolidated.” Or The soil whose present effective overburden pressure is less than that which the soil experienced in the past is called over consolidated soil.
23. Define pre-consolidation pressure.
The maximum effective past pressure is called pre-consolidation pressure.
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UNIT III - PART B (QUESTIONS)
A water tank is supported by a ring foundation having outer diameter of 10 m and inner diameter
of 7.5 m. the ring foundation transmits uniform load intensity of 160 kN/m2. Compute the vertical stress induced at depth of 4 m, below the centre of ring foundation, using
(i) Boussinesque analysis and
(ii) Westergaard’s analysis, taking μ = 0
A stratum of clay with an average liquid limit of 45% is 6m thick. Its surface is located at a depth of 8m below the ground surface. The natural water content of the clay is 40% and the specific gravity is 2.7. Between ground surface and clay, the subsoil consists of fine sand. The water table is located at a depth of 4m below the ground surface. The average submerged unit weight of sand
is 10.5 kN/m3 and unit weight of sand above the water table is 17 kN/m3. The weight of the building that will be constructed on the sand above clay increases the overburden pressure on the
clay by 40 kN/m2. Estimate the settlements of the building.
A concentrated point load of 200 kN acts at the ground surface. Find the intensity of vertical pressure at a depth of 10 m below the ground surface and situated on the axis of the loading. What will be the vertical pressure at a point at a depth of 5 m and at a radial distance of 2 m from the axis of loading? Use Boussinesque analysis.
Explain with a neat sketch the Terzhaghi’s one dimensional consolidation theory.
The load from a continuous footing of width 2m, which may be considered to be strip load of considerable length, is 200 kN/m2. Determine the maximum principal stress at 1.5m depth below the footing, if the point lies (i) directly below the centre of the footing, (ii) directly below the edge of the footing and (iii) 0.8m away from the edge of the footing.
6.What are different components of settlement? Explain in detail.
7.In a laboratory consolidometer test on a 20 mm thick sample of saturated clay taken from a site, 50% consolidation point was reached in 10 minutes. Estimate the time required for the clay layer of 5 m thickness at the site for 50% compression if there is drainage only towards the top. What is the time required for the clay layer to reach 50% consolidation if the layer has double drainage instead of single drainage.
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8.What are the various components of a settlement? How are these estimated?
9.Explain the Newmark’s influence chart in detail.
10. How will you determine pre-consolidation pressure?
11.How will you determine coefficient of compression index (CC) from an oedomoter test?
An undrained soil sample 30cm thick got 50% consolidation in 20 minutes with drainage allowed at top and bottom in the laboratory. If the clay layer from which the sample was obtained is 3m thick in field condition, estimate the time it will take to consolidate 50% with double surface drainage and in both cases, consolidation pressure is uniform.
Derive Boussinesque equations to find intensity of vertical pressure and tangential stress when a concentrated load is acting on the soil.
14.A line load of 100 kN/m run extends to a long distance. Determine the intensity of vertical stress at a point, 2 m below the surface and
Directly under the line load and
At a distance 2 m perpendicular to the line.Use Boussinesq’s theory.
15.Explain in detail the laboratory determination of co-efficient of consolidation.
A layer of soft clay is 6 m thick and lies under a newly constructed building. The weight of sand overlying the clay layer produces a pressure of 2.6 kg/cm2 and the new construction increases the pressure by 1.0 kg/cm2. If the compression index is 0.5. Compute the settlement. Water content is 40% and specific gravity of grains is 2.65.
Explain the principle of Newmark’s Chart in detail.
Explain in detail with sketches the applications of Boussinesq theory.
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U NIT IV - SHEAR STRENGTH
PART A (TW O MARKS QUESTIONS WITH ANSWERS)
1. Write down the Mohr’s-Cou lomb failure envelope equation.
The Mohr–Coulomb failure critterion represents the linear envelope that is obtained from a plot of the shear strength of a material versus the applied normal stress. This relatio n is expressed as
where is the shear strength, is the normal stress, is the intercept of the failure envelope with the axis, and is the slope of the failure envelope. The quantity is often called the cohesion and the angle is called the angle of internal friction.
Why triaxial shear test is co nsidered better than direct shear test?
The soil samples are subjected to uniform stresses and strains.
Different combinations of confining and axial stresses can be applied.
Drained and undrained te sts can be carried out.
Pore water pressures can be measured in undrained tests.
The complete stress-strain behaviour can be determined.
What are different types of t riaxial compression tests based on drainage conditions?
UU (unconsolidated undrained ) test: In this, cell pressure is applied without a llowing drainage. Then keeping cell pressure constant, deviator stress is increased to failure witho ut drainage.
CU (consolidated undrained) t est: In this, drainage is allowed during cell pre ssure application. Then without allowing further drainage, deviator stress is increased keeping cell pressure constant.
CD (consolidated drained) te st: This is similar to CU test except that as deviator stress is increased, drainage is permitted. The rate of loading must be slow enough to ensure no excess pore water pressure develops.
In the UU test, if pore water pres sure is measured, the test is designated by UU.
In the CU test, if pore water pre ssure is measured in the second stage, the test is symbolized as CU.
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4. Explain the Mohr–Coulomb failure theory.
The Mohr–Coulomb failure crit erion represents the linear envelope that is obt ained from a plot of the shear strength of a material versus the applied normal stress. This relation is expressed as
.Where
is the shear strength,
is the normal stress,
is the intercept
of the failure envelope with
theaxis, and
is
the slope of the failure
envelope. The
quantity is often called the co hesion and the angle is called the angle of internal friction. Compression is assumed to be p ositive in the following discussion. If compress ion is assumed to be negative then should be re placed with .
5. State the principles of direct shear test.
A direct shear test is a laborato ry or field test used by geotechnical engineers to measure the
shear strength properties of soil or rockmaterial, or of discontinuities in soil or rock
masses.Direct shear tests can b e performed under several conditions. The a dvantages of the direct shear test over other shea r tests are the simplicity of setup and equipm ent used, and the
ability to test under differing saturation, drainage, and consolidation c onditions. These
advantages have to be weighed against the difficulty of measuring pore-wat er pressure when testing in undrained conditions, and possible spuriously high results from fo rcing the failure
plane to occur in a specific locat ion.
6. What is shear strength of so il?
Shear strength is a term used in soil mechanics to describe the magnitude of the shear stress that a soil can sustain. The shear resi stance of soil is a result of friction and interlocking of particles, and possibly cementation or bonding at particle contacts.
7. How will you find the shear strength of cohesionless soil?
The shear strength parameters of soil can be determined in the laboratory p imarily by three types of tests. Direct shear test, triaxial test and unconfined compression test . By using direct shear test, we can find the shear strength of cohesionless soil.
8. How will you find the shear strength of cohesive soil?
By using triaxial test and unc onfined compression test
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9. What is the effect of pore pressure on shear strength of soil?
Subsurface water is divided into zones of positive and negative pore pressures. The dividing line is the groundwater table (also known as phreatic surface) where the pressure is equal to atmospheric pressure. Below the groundwater table, the soil is fully saturated, and the pore pressure is above atmospheric pressure and positive in value. Above the groundwater table where the soil is unsaturated, the pore pressure is below atmospheric pressure and hence is negative in value. In this zone, the pore water is continuous or semi continuous and the pore water pressure is below atmospheric pressure. The magnitude of the negative pore pressure (sometimes called soil suction) is controlled by surface tension at the air-water boundaries within the pores and is governed by grain size. In general, the finer the soil particles, the larger the saturation capillary head, and hence the higher the negative pore pressure. Rainfall infiltration from the ground surface may rapidly reduce the magnitude of negative pore pressure. Any change in these pore pressures alters alter the shear strength of soil and therefore has a tremendous effect on the slope stability. By lowering effective stress, positive pore pressure reduces the available shear strength within the soil mass thereby decreasing the slope stability.
10. List out the types of shear tests based on drainage.
Consolidated Drained (CD) In a consolidated drained test the sample is consolidated and sheared in compression results in drainage. The rate of axial deformation is kept constant, i.e. is strain controlled. The idea is that the test allows the sample and the pore pressures to fully consolidate (i.e. adjust) to the surrounding stresses. The test may take a long time to allow the sample to adjust, in particular low permeability samples need a long time to drain and adjust strain to stress levels.
Consolidated Undrained (CU) In a consolidated undrained test the sample is not allowed to drain. The shear characteristics are measured under undrained conditions and the sample is assumed to be fully saturated.
Unconsolidated Undrained (UU)
In an unconsolidated undrained test the sample is not allowed to drain. The sample is compressed at a constant rate (strain-controlled).
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Write down the Coulomb’s expression for shear strength.
What are the advantages of Tri-axial Compression Test?
The stress distribution on the failure plane is uniform.
The specimen is free t o fail on the weakest plane
There is complete con trol over the drainage.
Pore pressure changes and the volumetric changes can be measured directly.
v. The state of stress at a ll intermediate stages upto failure is known. Th e Mohr circle can be drawn at any stage of shear.
vi. This test is suitable f or accurate research work and the apparatus ad aptable to special requirements such as ext ension test and tests for different stress paths.
13. Define ‘angle of repose’ of soil.
The angle of repose or the critical angle of repose of a granular material is the steepest angle of descent or dip relative to the horizontal plane to which a material can be piled w ithout slumping. At this angle, the material on the slope face is on the verge of sliding. The an gle of repose can range from 0° to 90°. Smooth, rounded sand grains cannot be piled as steeply as can rough, interlocking sands. If a small a mount of water is able to bridge the gaps between particles, electrostatic attraction of the water to mineral surfaces will increase soil strength .
14. Define shear strength and failure envelope.
Shear strength is a term used in soil mechanics to describe the magnitude of the shear stress that a soil can sustain. The shear resi stance of soil is a result of friction and interlocking of particles, and possibly cementation or bonding at particle contacts.The Mohr–Coulomb failure criterion represents the linear envelope that is obtained from a plot of the shear stren gth of a material versus the applied normal stress. This relation is expressed as
15. Define Cohesion and stress path.
Cohesion of soil is an important factor of soil consistency. For example, d efines it as "the cohesive force that takes place between adjacent particles".Cohesion means "t he shear strength
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when the compressive stresses are equal to zero".Series of stress points connected by a line or curve is called stress path.
18. What is angle of internal friction?
A measure of the ability of a unit of rock or soil to withstand a shear stress. It is the angle (φ), measured between the normal force (N) and resultant force (R), that is attained when failure just occurs in response to a shearing stress (S).Its tangent (S/N) is the coefficient of sliding friction. Its value is determined experimentally.
19. What are the various methods of determination of shear strength in the laboratory?
Direct shear test.
Triaxial shear test
Unconfined compression test.
Vane shear test.
20. What are the disadvantages of direct shear test?
The advantages of the direct shear test over other shear tests are the simplicity of setup and equipment used, and the ability to test under differing saturation, drainage, and consolidation conditions. These advantages have to be weighed against the difficulty of measuring pore-water pressure when testing in undrained conditions, and possible spuriously high results from forcing the failure plane to occur in a specific location.
21. When is vane shear test adopted?
Vane shear test is a useful method of measuring the shear strength of clay.
It is a cheaper and quicker method. The test can also be conducted in the laboratory.
The laboratory vane shear test for the measurement of shear strength of cohesive soils, is useful
for soils of low shear strength (less than 0.3 kg/cm2) for which triaxial or unconfined tests cannot be performed.
The test gives the undrained strength of the soil.
The undisturbed and remoulded strength obtained are useful for evaluating the sensitivity of soil.
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22. Sketch the Mohr’s circle for total stresses for undrained unconsolidatedtriaxial test.
24. Sketch the failure envelope for drained triaxial test.
UNIT IV - PART B (QUESTIONS)
Obtain the relationship between the principal stresses in triaxial compression test using Mohr-Coulomb failure theory.
Two identical soil specimens were tested in a triaxial apparatus. First specimen failed at a deviator
stress of 770 kN/m2 when the cell pressure was 2000 kN/m2. Second specimen failed at a deviator
stress of 1370 kN/m2 under a cell pressure of 400 kN/m2. Determine the value of c and
Φ analytically. If the same soil is tested in a direct shear apparatus with a normal stress of 600 kN/m2, estimate the shear stress at failure.
3. Write down a step by step procedure for determination of cohesion of a given clayey soil by conducting unconfined compression test.
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A saturated specimen of cohesion less sand was tested in triaxial compression and the sample
failed at a deviator stress of 482 kN/m2 when the cell pressure was 100 kN/m2 under the drained conditions. Find the effective angle of shearing resistance of sand. What would be the deviator stress and the major principal stress at failure for another identical specimen of sand, if it is
tested under cell pressure of 200 kN/m2. Use either Mohr’s circle method or analytical method.
Explain with neat sketches the procedure of conducting direct shear test. Give its advantages over other methods of finding shear strength of soil.
(i) Write a brief critical note on unconfined compression test.
(ii) What are the advantages and disadvantages of triaxial compression test.
A vane, 10 cm long and 8 cm in diameter, was pressed into soft clay at the bottom of a bore hole. Torque was applied and gradually increased to 45 N-m when failure took place. Subsequently, the vane rotated rapidly so as to completely remould the soil. The remoulded soil was sheared at a torque of 18 N-m. Calculate the cohesion of the clay in the natural and remoulded states and also the value of the sensitivity.
Describe the triaxial shear test. What are the advantages of triaxial shear test over the direct shear test?
Explain the Triaxial compression test to determine the shear strength of soil.
Explain drained behavior of clay with reference to shear strength.
Explain the direct shear test to determine the shear strength of soil.
Explain the Mohr-Coulomb failure theory.
Explain with neat sketch Direct Shear method of finding Shear Strength.
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The following data were obtained in a direct shear test. Normal pressure 20 kN/m2, Tangential
pressure = 16 kN/m2, Angle of internal friction = 200, Cohesion = 8 kN/m2. Represent the data by Mohr’s circle and compute the principal stresses and the direction of
principal planes.
Compare the merits and demerits oftriaxial compression test.
A particular soil failed under a major principal stress of 300 kN/m2 with a corresponding minor
principal stress of 100 kN/m2. If for the same soil, the minor principal stress had been200 kN/m2.
Determine what the major principal stress would have been if (i) Φ = 300 and(ii) Φ = 00.
A Cylindrical specimen of dry sand was tested in a triaxial test. Failure occurred under a cell
pressure of 1.2 kg/cm2 and at a deviator stress of 4.0kg/cm2. Find(i) Angle of shearing resistance of the soil.(ii) Normal and shear stresses on the failure plane.(iii) The angle made by the plane with the minor principal plane.(iv) The maximum shear stress on any plane in the specimen at the instant of failure.
Explain in detail the determination of shear strength using unconfined compression test.
Explain in detail the determination of shear strength using vane shear test.
Explain the shear strength behavior of cohesive and cohesionless soils under different drainage condition in a triaxial test.
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UNIT V- SLOPE STABILITY
PART A (TWO MARKS QUESTIONS WITH ANSWERS)
1. Differentiate finite slope and infinite slope.
Infinite slope:
Slopes extending to infinity do not exists in nature. For all practical purposes any slope of great extent with soil conditions essentially same for all identical depth below the surface are known as infinite slopes.
Finite slope:
A finite slope is one with a base and top surface, the height being limited. The inclined faces of earth dams, embankments and excavation and the like are all finite slopes.
2. Write down the expression for factor of safety of an infinite slope in case of cohesion-less soil.
F = τf / τ = tanφ / tani
What are different factors of safety used in the stability of slopes?
Factor of safety against sliding.
Factor of safety against failure.
Factor of safety with respect to cohesion.
List out any two slope protection methods.
Retaining walls and Piles.
Cut and fill solutions
Support and reinforcing systems.
Drainage control
Surface protection of slopes.
Vegetation
Surface covering.
Define critical surface of failure.
The surface corresponding to minimum factor of safety is the critical surface of failure.
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6. What do you mean by Tension crack?
The existence of tension cracks is likely to increase the tendency of a soil to fail. The length of failure surface along which shear strength can be mobilized is reduced. In addition a crack may be filled with water (e.g., due to rainfall). The additional force due to water pressure in a crack increases the tendency for a slip to occur.
Cracks open up in cohesive soils due to the soil’s low tensile strengths; the depth of these cracks can theoretically be found by
Zc= 2c/γ tan2 (45°+φ/2) ,Zc= depth of tension crack, c = cohesion, Φ = angle of friction
γ = unit weight of the soil material.
7. What is a stability number? What are the uses of stability charts?
The dimensional quantity Sn =c / Fc γ H. A dimension-less parameters called a stability number is often useful for analysis of slope of c-φ soil.
Stability charts show a range of stability characteristics for slopes with various soil properties and shapes.
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8. State the two basic types of failure occurring in finite slopes.
Rotational failure and Translation failure are the two basic types of failure occurring in finites slopes. Other failures are1. Slope failure
i. Face failure ii. Toe failure 2. Base failure.
9. What is a slide?
The failure of a mass of soil located beneath a slope is called a slide.
What are the different types of Slope failure?
Rotational failure
Translation failure
Compound failure
Wedge failure.
What are the types of slopes?
Infinite slopes.
Finite slopes.
What are the various methods of analysis of finite slopes?
Planar failure surface :
Culmann’s method.
2) Circular failure surface :
Swedish slip circle method.
Friction circle method.
Bishop’s method.
13. Define factor of safety and critical depth. Factor of safety:
Factor of safety = Shearing strength along the surface / Magnitude of shearing stress at most
severely stressed internal surface. = τf / τ.
Critical depth:
The depth corresponding to minimum factor of safety is said to be critical depth.
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14. What are the types and causes for slope failure?
Types:
Rotational failure
Translation failure
Compound failure
Wedge failure.
Face failure
Toe failure.
Causes:
Erosion.
Rainfall.
Earthquakes.
Geological factors.
External loading.
Construction activities such as excavation of slopes and filling of slopes.
Rapid drawdown (a lowering of water table)
Increment of pore water pressure.
The change in topography.
List out the types of slope failure with figure.
Face failure
Toe failure
Base failure
What are the factors affecting slope stability?
Slope stability is affected by the following factors.
Strength of soil and rock.
Type of soil and stratification.
Discontinuities and planes of weakness.
Groundwater table and seepage through the slope.
External loading.
Geometry of the slope.
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17. What are the methods to improve and protect slope stability?
Slope stability can be improved by taking following actions.
Slopes are made flattened or benched.(Weight provided at toe.)
Lowering of ground water table to reduce pore pressure in the slope.
Use of driven or cast-in place piles.
Retaining wall or sheet piling provided to increase resistance to sliding.
State some of the slope protection measures.
Slope flattening reduces the weight of the soil mass tending to slide.
Drainage helps in reducing the seepage flows and hence increases the stability.
Densification by use of vibro floatation explosives helps in increasing the stability of slopes in cohesiveness soils.
An infinite slope with a slope angle of 30° is 5 m high. The soil has cohesion of 30 kPa, angle
of internal friction of 20° and unit weight of 19kN/m3. Find the factor of safety with respect to cohesion.
Solution:Sn =c / Fc γ H.
Sn= cos2i (tani-tanφ) = cos230 (tan30-tan20) = 0.16 0.16 = 30 /19 x Hc
Hc = 9.87 m
FH = Fc = 9.87 / 5 = 1.97.
20. What are the three critical cases for which stability analysis is carried out for side
slopes of an earth dam?
Stability of downstream slope during steady seepage.
Stability of upstream slope during sudden drawdown.
Stability of both upstream and downstream slopes during and immediately after construction.
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UNIT IV - PART B (QUESTIONS)
1. Explain the procedure to calculate the factor of safety of a finite slope possessing both cohesion and friction (c - Φ) by method of slices.
2.A slope is to be constructed in a soil for which c = 0 and Φ = 36°. It is to be assumed that the water level may occasionally reach the surface of a slope with seepage taking place parallel to the slope. Determine the maximum slope angle for a factor of safety 1.5,assuming a potential failure surface parallel to the slope. What would be the factor of safety of the slope, constructed at this angle, if the water table should be below the surface? The saturated unit weight of the soil
is 19 kN/m3.
3.A new canal is excavated to a depth of 5 m below ground level through a soil having the
following characteristics: C = 14 kN/m2; Φ = 15°; e = 0.8 and G = 2.70. The slope of banks is 1 in 1. Calculate the factor of safety with respect to cohesion when the canal runs full. If it is suddenly and completely emptied, what will be the factor of safety?
4.Write down the procedure for determining the factor of safety of a given slope by friction circle method.
5.A canal is to be excavated to a depth of 6m below ground level through a soil having the following characteristics c = 15 kN/m2, Φ = 20°, e = 0.9 and G = 2.67. The slope of the banks is 1 in 1. Determine the factor of safety with respect to cohesion when the canal runs full. What will be the factor of safety if the canal is rapidly emptied completely?
6.Explain with neat sketches the Bishop’s method of stability analysis.
7.What are different types of slope failures? Discuss the various methods for improving the stability of slopes.
8.An embankment 10 m high is inclined at 35º to the horizontal. A stability analysis by the method of slices gave the following forces: ΣN = 900kN, ΣT = 420kN, ΣU = 200kN. If the
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length of the failure arc is 23.0 m, find the factor of safety. The soil has c = 20kN /m2 and Φ =
15º.
Explain the Swedish slip circle method in detail. (10)
Explain Taylor’s stability number and its applicability. (6)
Explain in detail the friction circle method of stability analysis for slopes with sketch.
Explain any four methods of slope protection. (8)
13.A cut 9 m deep is to be made in clay with a unit weight of 18 kN/m3 and cohesion of 27
kN/m2. A hard stratum exists at a depth of 18 m below the ground surface. Determine from Taylor’s charts if a 300 slope is safe. If a factor of safety of 1.50 is desired, what is a safe angle of slope?
Explain in detail the various methods to protect slopes from failure.
Explain in detail the Swedish circle method of stability analysis.
Explain in detail the friction circle method of stability analysis.
Explain in detail the Bishop’s method of stability analysis.
Explain in detail about Taylor’s stability number and stability curves.
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