DHANALAKSHMI COLLEGE OF ENGINEERING, CHENNAI DEPARTMENT OF CIVIL ENGINEERING CE6405 SOIL MECHANICS UNIT I : SOIL CLASSIFICATION AND COMPACTION

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1 DHANALAKSHMI COLLEGE OF ENGINEERING, CHENNAI DEPARTMENT OF CIVIL ENGINEERING CE6405 SOIL MECHANICS UNIT I : SOIL CLASSIFICATION AND COMPACTION PART A (2 marks) 1. Define Void ratio, Porosity and Degree of Saturation (N-10) Void ratio е of a given soil sample is the ratio of the volume of voids to the volume of soil solids in the given soil mass. Porosity n of a given soil sample is the ratio of the volume of voids to the total volume of the given soil mass. Degree of Saturation S is defined as the ratio of the volume of water present in a given soil mass to the total volume of voids in it. 2. Distinguish between Residual and Transported soil (M-12) 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 materials derived from plants and animals living in the area. Transported Soil A soil that has been transported (eroded) then deposited in a region where it was not originally formed. Transported soils are the result of erosion and deposited by wind, water and ice. Transported soils may have properties very difficult 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.

2 3. What is a zero air voids line? Draw a compaction curve and show the zero air voids line (N-11) The zero air voids (ZAV) line is the combination of moisture and density that produce complete saturation of the soil or the γd obtained when there is no air in the void spaces. The compaction curve theoretically does not cross this line but becomes parallel to it. 4. Relation between γsat, G, γw and e (M-12) sat G e 1 e γsat = Saturated unit weight G = Specific gravity w γw = Unit weight of water e = Volume of voids 5. If a soil sample is having porosity 40% and degree of saturation 80%, find its percentage air voids. Given: n = 40%; S = 80%; Solution: Air content, ac = 1 S = = 0.2 % air voids, na = n x ac = 0.4 x 0.2 = 0.08 = 80% 6. The dry density of a soil and its specific gravity of solids are respectively 18kN/m 3 and 2.7. Find the moisture content required to have 100% saturation of the soil. Given: γd = 18 kn/m 3 ; G = 2.7; Assume S = 100%; Solution: 7. A dry soil sample weighing 70gm. Total volume of sample is 40ml. Specific gravity of soil is Find volume of voids and void ratio.

3 Given: Solution: Volume of soil solids Volume of voids Void ratio 8. An undisturbed soil sample has a plastic limit 25%, a natural moisture content of 40% and a liquidity index of 50%. Find its liquid limit. Given: Solution: wp = 0.25; w = 0.4; IL = 0.5; 9. A compacted sample of soil with a bulk unit weight of 19.62kN/m 3 has a water content of 15 per cent. What are its dry density, degree of saturation and air content? Assume G=2.65. (M-10) Given: γ = kn/m 3 w = 15% G = 2.65 Solution: a) γd = (γ / 1+w) = kn/m 3 b) e = (Gs γw / γd) 1 = 0.52 c) S = wgs/e = or 75.86% d) ac = 1 S = or 24.14% 10. List the Index Properties of soil i. Water content ii. Specific gravity

4 iii. Particle size distribution iv. Consistency limits v. In-situ density vi. Density index 11. What are the factors affecting compaction? i. The moisture content ii. The compactive effect iii. The type of soil iv. The method of compaction 12. State the methods to determine water content of the soil. (i) Oven drying method (ii) Sand bath method (iii) Alcohol method (iv) Calcium carbide method (v) Pyconometer method (vi) Radiation method (vii) Torsion balance method 13. Limitations of sedimentation analysis The analysis is based on the assumptions that, (i) Soil particles are spherical, (ii) Particles settle independent of other particles and the neighboring particles do not have any effect on its velocity of settlement and The walls of jar, in which the suspension is kept, also do not affect the settlement.

5 14. What are the Atterberg limits for soil and why it is necessary (N-12) Liquid limit Plastic limit Shrinkage limit The Atterberg limits can be used to distinguish between silt and clay, and it can distinguish between different types of silts and clays. 15. Two clays A and B have the following properties: Clay A Clay B Liquid limit 44 per cent 55 per cent Plastic limit 29 per cent 35 per cent Natural water content 30 per cent 50 per cent Which of the clays, A or B, would experience larger settlement under identical loads? Why? (M-10) Using equation: IC = (WL W) / IP For Clay A IC = 0.93; For Clay B IC = 0.25 Since the consistency index of clay B is low when compared clay A, thereby clay B will undergo larger settlements. 16. Various systems used for classifying grain size (i) (ii) (iii) (iv) U.S.Bureau of Soil and Public Road Administration (PRA) System of United States, International soil classification, proposed at the International Soil Congress at Washington, D.C. in 1927, and The M.I.T. classification proposed by Prof.Gilboy of Massachusetts Institute of Technology as a simplification of the Bureau of Soils Classification, and Indian Standard Classification (IS: ) based on the M.I.T. system. These four systems. 17. Determine the maximum possible voids ratio for a uniformly graded sand of perfectly spherical grains. (N-11) 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. 3 Volume = 6 d Total volume = 1x1x1=1 No. of solids = 1/dx 1/d x 1/d = 1/d 3 Volume of solids Vs = Volume of voids Vv = 1- Vs e = Vv/Vs = n 1 e e 6 d 3 1 x d 3 6

6 18. Define degree of saturation and shrinkage ratio. (N 14) It is defined as the ratio of a given volume change expressed as a percentage of dry volume, to the corresponding change in water content above the shrinkage limit expressed as a percentage of the weight of the oven dried soil. 19. Define specific gravity and density index. The term density index is defined as the ratio of the difference between the voids ratio of the soil in its loosest state emax and its natural voids ratio e to the difference the voids in the loosest and densest states. Specific gravity G is defines as the ratio of the weight of a given volume of soil solids at a given temperature to the weight of an equal volume of distilled water at that temperature, both weights being taken in air. 20. What do understand from grain size distribution? The grain size analysis is widely used in classification of soils. The data obtained from grain size distribution curves is used in the design of filters for earth dams and to determine suitability of soil for road construction, air field etc. Information obtained from grain size analysis can be used to predict soil water movement although permeability tests are more generally used. 21. What are consistency limits of soil? Shrinkage limit Plastic limit Liquid limit 22. Define plasticity index, flow index and liquidity index. It is defined as the numerical difference between the liquid limit and the plastic limit of a soil. Ip = wl wp 23. What are the methods available for determination of in-situ density? (1) Sand replacement method (2) Core cutter method (3) Water displacement method (4) Rubber balloon method 24. What is the function of A-line Chart in soil classification? The A-line separates clay from silt and organic soil from inorganic soil. 25. Write the major soil classifications as per Indian Standard Classification System.

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8 PART - B (16 Marks) 1. Write down a neat procedure for determining water content and specific gravity of a given soil in the laboratory by using a pycnometer. (N-12) 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. (N-12) 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 Natural water content 32% 40% Find which soil is (i) More plastic. (ii) Better foundation material on remoulding. (iii) Better shear strength as function of water content. (iv) Better shear strength at plastic limit. Classify the soil as per IS classification system. Do those soils have organic matter? (M-10) 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 G 1 es e w (M-10) 5. The mass of wet soil when compacted in a mould was 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 = (M-12) 6. 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 Assuming the viscosity and unit weight of water at the temperature of the test as Ns/m 2 and 9.81 kn/m 3 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. (M-12) 7. 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 m 3 respectively.

9 Calculate the volume of soil to be excavated from each pit. Which borrow pit is the most economical? (Take G = 2.65). (N-11) 8. A laboratory compaction test on soil having specific gravity equal to 2.67 gave a maximumdry unit weight of 17.8 kn/m 3 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? (N-11) 9. A soil sample has a porosity of 40 per cent. The specific gravity of solids is calculate i) Voids ratio ii) Dry density and iii) Unit weight if the soil is completely saturated. (M-11) 10. A soil has a bulk unit weight of KN/m 3 and water content of 15 percent. Calculate the water content of the soil partially dries to a unit weight of KN/m 3 and the voids ratio remains unchanged. (M-11) 11. Explain Standard Proctor Compaction test with neat sketches. (N-10)

10 UNIT II : SOIL WATER AND WATER FLOW PART A (2 Marks) 1. What are the different types of soil water? (M-12) Broad Classification 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 2. List out the methods of drawing flow net. (M-12) (a) Graphical method (b) Electrical analogy method (c) Flow tank model (d) Viscous model 3. What is meant by total stress, neutral stress and effective stress? (N 12) Total stress is the total load per unit area. It is due to self-weight of soil and overburden pressure on the soil. The total stress consists of two components: effective stress and neutral stress or pressure. Effective stress is the pressure transmitted from particle through their point of contact through the soil mass. It is effective in decreasing the void ratio and mobilising its shear strength. The neutral stress or pore water pressure is the pressure transmitted through pore fluid. σ = σ + u 4. State and explain Darcy s law. (A-10) The law of flow of water through soil was first studied by Darcy (1856) who demonstrated experimentally that for laminar flow conditions in a saturated soil, the rate of flow or the discharge per unit time is proportional to the hydraulic gradient. A = total c/s area of soil mass i = hydraulic gradient k = Darcy s coefficient of permeability v = velocity of flow or average discharge velocity 5. What is quick sand? How would you calculate the hydraulic gradient required to create quick sand conditions in a sample of sand? (N-11)

11 If the seepage pressure becomes equal to the pressure due to submerged weight of the soil, the effective pressure is reduced to zero. In such a case, a cohesionless soil loses its shear strength, and the soil particles have a tendency to move up in the direction of flow. This phenomenon of lifting of soil particles is called quick condition, boiling condition or quick sand. 6. 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. (N-11) Q = k H (Nf / Nd) H = 52-2 = 50m K = 3 x 10-5 m/sec, Nf = 4, Nd = 25 Q = 3 x 10-5 x 50 x (4/25) = m 3 /sec 7. What is capillary rise? (N-12) The rise of water in the capillary tubes, or the fine pores of the soil, is due to the existence of surface tension which pulls the water up against the gravitational force is determined as capillary rise. The height of capillary rise, above the ground water surface depends upon the diameter of the capillary tube the value of the surface tension. 8. What is surface tension? (A-11) Surface tension of water is the property which exists in the surface film of water tending to contract the contained volume into a form having a minimum superficial area possible. The surface tension Ts is approximately equal to 72.8 dynes per cm or 0.728x10-6 kn/cm at 20 o C 9. Write down the uses of Flow net. (N-10) Determination of seepage pressure 10. What is seepage velocity? (M-13) Seepage velocity vs, is defined as the rate of discharge of percolating water per unit c/s area of voids perpendicular to the direction of flow. 11. Find the capillary rise in a sandy soil which has a void ratio of 0.65 and the effective size of particle is 0.07mm. Take C = 0.1 cm 2. Given: e = 0.65; D10 = 0.07mm = 0.007cm; C = 0.1 cm 2 ; Solution: 12. Define permeability. It is defined as the property of a porous material which permits the passage or seepage of water through its interconnecting voids. A material having continuous voids is called permeable.

12 13. What are the factors affecting permeability? (a) Grain size (b) Properties of the pore fluid (c) Voids ratio of the soil (d) Structural arrangement of the soil particles (e) Entrapped air and foreign-matter and (f) Adsorbed water in clayey soils 14. What are the methods available for determination of permeability? Laboratory methods: (a) Constant head permeability test (b) Falling head permeability test Field methods: (a) Pumping-out test (b) Pumping-in test Indirect methods: (a) Computation from grain size or specific surface (b) Horizontal capillarity test 15. The critical hydraulic gradient of a sandy soil having specific gravity of solids of 2.7 is 1.0. Find its porosity. Given: ic = 1.0; G = 2.7; Solution:

13 16. Define discharge and seepage velocity (N-10) Discharge velocity or velocity of flow v is the rate of discharge of water per unit of total c/s area A of soil. This total area of c/s is composed of the area of solids As and area of voids Av. Seepage velocity vs, is defined as the rate of discharge of percolating water per unit c/s area of voids perpendicular to the direction of flow. 17. Coefficient of permeability and Coefficient of transmissibility (N-09) It is defined as the velocity of flow which will occur through the total c/s area of the soil under a unit hydraulic gradient. It is represented by k. It is defined as the rate of flow of water through a vertical strip of aquifer of unit width and extending the full saturation height under unit hydraulic gradient. It is represented by T. 18. Loose uniform sand with rounded grains has an effective grain size D10 equal to 0.3 mm. Estimate the coefficient of permeability? Given: D10 = 0.3mm = 0.03cm; Solution: From Jaky s formula, 19. Assumptions and limitations of Dupuit s theory i. The velocity of flow is proportional to the tangent of the hydraulic gradient instead of its sine. ii. The flow is horizontal and uniform everywhere in the vertical section. iii. Aquifer is homogeneous, isotropic and of infinite aerial extent. iv. The well penetrates and receives water from the entire thickness of the aquifer. v. The coefficient of transmissibility is constant at all places and at all times. vi. Natural ground water regime affecting an aquifer remains constant with time. vii. Flow is laminar and Darcy s law is valid. 20. Define bulking of sand. If a dry mass of sand is moistened slightly and then shovelled or dumped loose into a heap, its volume will increase considerably relative to dry state. This phenomenon is called bulking of sand. 21. List out the methods of drawing flow net. (e) Graphical method (f) Electrical analogy method (g) Flow tank model (h) Viscous model

14 22. Define velocity potential and stream function. (N-13) The velocity potential may be defined as a scalar function of space and time such that its derivative with respect to any direction gives the fluid velocity in that direction. Stream function ψ is defined as a scalar function of space and time such that a partial derivative of this function with respect any direction gives the velocity component in a direction +90o to the original direction. 23. What is quick sand? How would you calculate the hydraulic gradient required to create quick sand conditions in a sample of sand? (N-11) The phenomenon of lifting of soil particles is called quick sand. Hydraulic gradient of a quick sand condition is calculated by, 24. What are the applications of flow net? (a) Determination of seepage (b) Determination of hydraulic pressure (c) Determination of seepage pressure (d) Determination of exit gradient 25. What is meant by phreatic line? (N-13) The phreatic line or seepage line is defined as the line within a dam section below which there are positive hydrostatic pressures in the dam. The hydrostatic pressure on the phreatic line itself is atmospheric. The phreatic line can be located by (i) analytical method, (ii) graphical method and (iii) experimental method.

15 PART B (16 marks) 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 19.62kN/m 3. 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. (N-12) 2. Write down the procedure for determination of permeability by constant head test in the laboratory. (N-12) 3. 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 (M-10) 4. 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? (M-10) 5. 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 kn/m 3. The unit weight of clay may be assumed as kn/m 3 (M-12) 6. 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 Calculate seepage velocity of water during the test. (M-12) 7. The following data were recorded in a constant head permeability test. (N-11) Internal diameter of permeameter = 7.5 cm

16 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 discharge velocity and seepage velocity during the test. 8. Explain the falling head permeability test. (M-11) 9. What are the applications of flow net and explain briefly? (M-11) 10. A stratified soil deposit is shown in Fig.1. 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 (i) Discharge value and discharge velocities in each layer for horizontal flow and (ii) Hydraulic gradient and loss in head in each layer for vertical flow. (N-10)

17 UNIT III STRESS DISTRIBUTION AND SETTLEMENT PART A (2 Marks) 1. Write down Boussinesq equation for finding out the vertical stress under a single concentrated load. (N-12) (i) The soil mass is an elastic medium for which the modulus of Elasticity, E is constant. (ii) 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. (iii) The soil mass is isotropic, that is it has identical elastic properties in all directions through any point of it. (iv) The soil mass is semi infinite, that is it extends infinitely in all directions below a level surface. 2. Define normally consolidated clays and over consolidated clays. (M-15) If the present effective overburden pressure in the deposit is the maximum pressure to which the deposit has ever been consolidated at any time in the past, such a deposit is called a normally consolidated clay deposit. A clay soil deposit that has been fully consolidated under a pressure pc in the past, larger than the present overburden pressure po, is called an over-consolidated or pre-consolidated or pre-compressed clay deposit. 3. Explain the method of estimating vertical stress using Newmark s influence chart. (M-10) The plan of the loaded area is first drawn on a tracing sheet to the same scale as the scale of the line segment AB on the chart representing the depth z. The location of the point where the vertical stress is required is marked on the plan, say as P. Now, the tracing sheet is placed over the chart, such that the point P comes exactly over the center of the chart from where the rays are emanating. Now the number of mesh covered by the plan is counted. In case of partly covered mesh an intelligent judgement of the fraction of mesh covered is required. Let the total number of mesh be equal to n. Then the vertical stress at the desired depth is given by: 4. What are the assumptions made in Terzaghi s one dimensional consolidation theory? (M-10) (i) The soil mass is homogeneous (ii) The void spaces are completely filled with water (iii) The soil solids and water are incompressible (iv) Darcy s law is valid (v) The seepage flow and deformation are in one-dimensional direction (vi) Strains are small (vii) The permeability is constant over the range of effective stresses (viii) There is a unique pressure-void ratio relationship (ix) The time lag in consolidation is entirely due to the low permeability of the soil 5. What is the use of influence chart in soil mechanics? (M-11)

18 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 6. Differentiate between Compaction and Consolidation. (M-12) Compaction Consolidation (i) Removal of air voids (i) Removal of water voids (ii) Soil is partially saturated (ii) Soil is fully saturated (iii) Dynamic pressure is applied (iii) Static pressure is applied (iv) Suitable for cohesive and (iv) Suitable for cohesive soil cohesionless soil 7. What are isochrones? (N-11) The distribution of excess hydrostatic pressure at any time t is indicated by the curve, joining water levels, in the piezometric tubes, this curve is known as isochrone. 8. When a soil mass is said to be homogeneous? (A-11) If a soil mass contains similar particles or similar nature, then the soil is said to be homogeneous. 9. What are isobars? (A-11) An isobar is a curve or contour connecting all points below the ground surface of equal vertical pressure. An isobar is a spatial, curved surface of the shape of a bulb, because the vertical pressure on a given horizontal plane is the same in all directions at points located at equal radial distances around the axis of loading. 10. List the components of settlement in soil. (N-10) (i) Immediate settlement (Si) (ii) Settlement due to consolidation (Sc) (iii) Settlement due to secondary compression (Ss) 11. What are the two theories explaining the stress distribution on soil? (A-09) (i) Critical state theory (ii) Steady state theory

19 12. What is oedometer? (A-09) Oedometer is an instrument used for measuring the rate and amount of consolidation of a soil specimen under pressure. 13. What is meant by coefficient of volume change? The coefficient of volume change or the coefficient of volume compressibility mv, is defined as the change in volume of a soil per unit of initial volume due to a given unit increase in the pressure. 14. What is geostatic stress and pre-consolidation pressure? Stresses induced by the overburden pressure are called geostatic stresses. This situation gives rise to simple stress calculations when the ground surface is horizontal, and there is no marked variation of the soil properties in the horizontal direction. A Clay is said to be pre-compressed, pre-consolidated or over consolidated if it has ever been subjected to a pressure in excess of its present overburden pressure. The temporary overburden pressure to which a soil has been subjected and under which it got consolidated is known as pre-consolidation pressure. 15. What is a pressure bulb? The zone in a loaded soil mass bounded by an isobar of given vertical pressure intensity is called a pressure bulb. The vertical pressure at every point on the surface of pressure bulb is the same. 16. Write the equation of a uniformly loaded circular area of radius 1.5m with a pressure of 60kN/m 2 and thus obtain the exact depth at which the stress reduces to 10% of the applied stress. Solution: The vertical stress at a depth z under the centre of a circular area of diameter 2a is given as, Here σz = 0.10q. Therefore, the depth at which the stress is 10% of the applied stress is 5.48m.

20 17. Define co-efficient of compressibility and compression index. Co-efficient of Compressibility: It is defined as the decrease in voids ratio per unit increase of pressure, Compression index: The compression index represents the slope of the linear portion of the pressure voids ratio curve, and remains constant within a fairly large range of pressure. 18. What are the methods to determine co-efficient of consolidation? (i) Square root of time fitting method (ii) Logarithm of time fitting method (iii) Casagrande log time method (iv) Su s maximum slope method (v) Sivaram and Swamee s computational method 19. What are the factors influencing consolidation? (i) Permeability (ii) Compressibility (iii) Layer thickness (iv) Boundary conditions 20. Define Over consolidation ratio and creep. The ratio of (pc po) / po is called the over consolidation ratio (OCR). When the excess pore pressure due to consolidation has been dissipated, the change in voids ratio continues, but generally at a reduced rate. This phenomenon is known as secondary compression or secondary consolidation or creep. 21. A saturated clay layer with single drainage face takes 4 years to attain 50% degree of consolidation. What will be the time to attain 50% degree of consolidation if clay layer had double drainage? Solution: 22. Differentiate Consolidation and Compaction.

21 Compaction It is a dynamic process Compaction is almost instantaneous Densification is due to reduction of air voids Soil is always unsaturated For a specific compactive effort densification takes place only up to certain limiting water content called optimum moisture content Compaction is done before the construction of structure Consolidation It is a static process Consolidation is due to expulsion of pore water from voids Soil is considered to be completely saturated The process of consolidation starts as soon as the construction work begins

22 PART B (16 Marks) 1. 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 160kN/m 2. Compute the vertical stress induced at depth of 4 m, below the center of ring foundation, using (i) Boussinesque analysis and (ii) Westergaard s analysis, taking μ = 0 (M-10) 2. 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 10.5kN/m 3 and unit weight of sand above the water table is 17kN/m 3. The weight of the building that will be constructed on the sand above clay increases the overburden pressure on the clay by 40kN/m 2. Estimate the settlements of the building. 3. 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. (N-12) 4. Explain with a neat sketch the Terzhaghi s one dimensional consolidation theory. (N-12) 5. The load from a continuous footing of width 2m, which may be considered to be strip load of considerable length, is 200kN/m 2. 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. (M-12) 6. What are different components of settlement? Explain in detail. (M-12) 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. (N-11) 8. What are the various components of a settlement? How are these estimated? (N-11) 9. Explain the Newmark s influence chart in detail. (M-11)

23 10. How will you determine pre-consolidation pressure? (M-11) 11. How will you determine coefficient of compression index (CC) from an oedometer test? (M-11) 12. 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. (N-10) 13. Derive Boussinesque equations to find intensity of vertical pressure and tangential stress when a concentrated load is acting on the soil. (N-10) 14. Explain the assumptions made by Boussinesque in stress distribution on soils. (M-09) 15. A line load of 100kN/m run extends to a long distance. Determine the intensity of vertical stress at a point, 2 m below the surface and i) Directly under the line load and ii) At a distance 2 m perpendicular to the line. Use Boussinesq s theory. (M-09) 16. Explain in detail the laboratory determination of co-efficient of consolidation. (M-09) 17. 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 (M-09) UNIT IV SHEAR STRENGTH PART A (2 Marks) 1. Write down the Mohr s-coulomb failure envelope equation. (N-12)

24 Coulomb defined the function F (σ) as a linear function of σ and gave the following strength equation, Where, S = Shear stress; C = Cohesion; σ = normal stress; ϕ = angle of internal friction or shearing resistance. 2. Why triaxial shear test is considered better than direct shear test? (N-12) a) Progressive effects are less in the triaxial. b) The measurement of specimen volume changes are more accurate in the triaxial. c) The complete state of stress is assumed to be known at all stages during the triaxial test, whereas only the stresses at failure are known in the direct shear test. d) The triaxial machine is more adaptable to special requirements. 3. What are different types of triaxial compression tests based on drainage conditions? (M-10) Consolidated Drained (CD) Consolidated Undrained (CU) Unconsolidated Undrained (UU) 4. Explain the Mohr Coulomb failure theory. (M-10) The Mohr Coulomb failure criterion represents the linear envelope that is obtained from a plot of the shear strength of a material versus the applied normal stress. This relation is expressed as tan c Where is the shear strength, is the normal stress, c is the intercept of the failure envelope with the axis, and is the slope of the failure envelope. The quantity c is often called the cohesion and the angle is called the angle of internal friction 5. State the principles of direct shear test? (M-12) In principle, the shear box is an angel of friction test, in which one portion of soil is made to slide along another by the action of steadily increasing horizontal shearing force, while a constant load is applied normal to the plane of relative movement. To perform the test, a soil specimen is placed in a rigid square metal box, consisting of two halves. The lower half of the box can slide relative to the upper half when pushed or pulled by a motorised drive unit, while a yoke supporting a load hanger provides the normal pressure. 6. What is the effect of pore pressure on shear strength of soil? (M-12) When the pore pressure of the soil increases, there is a decrease in the effective stress which in turn reduces the shear stress also.

25 7. List out the types of shear tests based on drainage. (N-11) (a) Undrained test or quick test (b) Consolidated undrained test (c) Drained test 8. What is shear strength of soil? (M-11) The shear strength of soil is the resistance to deformation by continuous shear displacement of soil particles or on masses upon the action of a shear stress. Shear strength of a soil is equal to the maximum value of shear stress that can be mobilized within a soil mass without failure taking place. 9. Write down the laboratory methods to determine shear strength. Direct shear test Triaxial shear test Unconfined Compression test Vane shear test 10. How will you find the shear strength of cohesive soil? What are the advantages of Triaxial Compression Test? (M-11) (a) Undrained test on saturated cohesive soils (b) Undrained test on partly saturated cohesive soil (c) Consolidated-undrained test on saturated cohesive soils (d) Consolidated undrained test on partly saturated cohesive soils (e) Drained tests Advantages 1. The shear tests under all the three drainage conditions can be performed with complete control 2. Precise measurements of the pore pressure and volume change during the test are possible 3. The stress distribution on the failure plane is uniform The state of stress within the specimen during any stage of the test, as well as at failure is completely determinate

26 11. Define angle of repose of soil. (M-09) The angle of repose of a soil is the gradient of the slope at which the soil settles naturally. A firm soil will have a steeper angle of repose than a loose soil. 12. Write the expression for coulomb s law. Coulomb s law of shear strength: (M-09) Where, C = apparent cohesion σ = the normal stress φ = the angle of internal friction or shearing resistance of the soil. 13. Define shear strength and failure envelope. The shear strength of soil is the resistance to deformation by continuous shear displacement of soil particles or on masses upon the action of a shear stress. Shear strength of a soil is equal to the maximum value of shear stress that can be mobilized within a soil mass without failure taking place. 14. What are the shear strength parameters? The following are the shear strength parameters, C = Cohesion and ϕ = Angle of internal friction 15. Define Cohesion and stress path. The term cohesion refers to the attractive forces between individual clay particles in the soil. As shearing forces are applied to the specimen, the points representing the effective stresses will move away from the hydrostatic pressure line and the path traced out in the stress space by these points is called a stress path. 16. What is angle of internal friction? Measure of the resistance of soil to sliding along a plane, is called angle of internal friction or friction angle ϕ. Angle of internal friction mass depends upon following factors, (a) Shape of particles (b) Surface roughness

27 (c) Type of interlocking (d) Lateral pressure (e) State of packing 17. What are the various methods of determination of shear strength in the laboratory? (a) Direct shear test (b) Triaxial shear test (c) Unconfined compression test (d) Vane shear test 18. What is Thixotrophy of clays? Thixotrophy is defined as an isothermal, reversible, time-dependent process which occurs under constant composition and volume. This phenomenon is attributed to a process of softening caused by re-moulding followed by a timedependent regain of the original hard state. 19. What are the disadvantages of direct shear test? (N-14) (a) The stress condition across the soil sample are very complex (b) The distribution of normal stress and shearing stresses over the potential surface of sliding is not uniform (c) The stress is more at the edges and less in the centre (d) As the test progress, the area under shear gradually decreases (e) As compared to the triaxial test, there is little control on the drainage of soil (f) The plane of shear failure is predetermined, which may not be the weakest one (g) There is effect of lateral restraint by the side walls of the shear box 20. What are the types of triaxial test based on drainage conditions? Consolidated Drained (CD) Consolidated Undrained (CU) Unconsolidated Undrained (UU) 21. When is vane shear test adopted? The vane shear test is best adopted for measuring of low undrained shear strength of saturated clays. In particular, the test is very suitable for soft clays and may not give reliable results if the clay contains sand or silt.

28 22. Sketch the Mohr s circle for total and effective stresses for undrained triaxial test. 23. Sketch the failure envelope for drained triaxial test. (M-15) 24. A cylindrical sample of soil having cohesion of 0.8 kg/cm 2 and angle of internal friction of 20 o is subjected to a cell pressure of 1.0 kg/cm 2. Calculate the maximum deviator stress at which the sample will fail and the angle made by the failure plane with the axis of the sample. Solution: Angle made by the failure plane with the axis of the sample = αf = = 35 0.

29 PART B (16 Marks) 1. Obtain the relationship between the principal stresses in triaxial compression test using Mohr-Coulomb failure theory. (M-10) 2. Two identical soil specimens were tested in a triaxial apparatus. First specimen failed at a deviator stress of 770kN/m2 when the cell pressure was 2000kN/m 2. Second specimen failed at a deviator stress of 1370kN/m2 under a cell pressure of 400kN/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 600kN/m 2, estimate the shear stress at failure. 3. A saturated specimen of cohesion less sand was tested in triaxial compression and the sample failed at a deviator stress of 482kN/m 2 when the cell pressure was 100kN/m 2 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. (N-12) 4. Write down a step by step procedure for determination of cohesion of a given clayey soil by conducting unconfined compression test. (N-12) 5. Explain with neat sketches the procedure of conducting direct shear test. Give its advantages over other methods of finding shear strength of soil. (M-12) (i) Write a brief critical note on unconfined compression test. (ii) What are the advantages and disadvantages of triaxial compression test. 6. 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 remold the soil. The remolded soil was sheared at a torque of 18 N-m. Calculate the cohesion of the clay in the natural and remolded states and also the value of the sensitivity 7. Describe the triaxial shear test. What are the advantages of triaxial shear test over the direct shear test? 8. Explain the Triaxial compression test to determine the shear strength of soil. (M-11) 9. Explain drained behavior of clay with reference to shear strength. (M-11) 10. Explain the direct shear test to determine the shear strength of soil. (M-11)

30 11. Explain the Mohr-Coulomb failure theory. (M-11) 12. Explain with neat sketch Direct Shear method of finding Shear Strength (N-10) 13. The following data were obtained in a direct shear test. Normal pressure 20kN/m 2, Tangential pressure = 16kN/m2, Angle of internal friction = 200, Cohesion = 8kN/m 2. Represent the data by Mohr s circle and compute the principal stresses and the direction of principal planes.

31 UNIT V : SLOPE STABILITY PART A (2 Marks) 1. Differentiate finite slope and infinite slope. (N-12) If the slope is of limited extent, it is called a finite slope. If a slope represents the boundary surface of a semi-infinite soil mass, and the soil properties for all identical depths below the surface are constant, it is called an infinite slope. 2. Write down the expression for factor of safety of an infinite slope in case of cohesion less soil. (A-10) 3. List out any two slope protection methods. (N-12) Slopes have been protected by adopting some successful techniques. In general, (a) Reducing the mass or loading which contributes to sliding (b) Improving the shearing strength along the anticipated zone of failure (c) Providing certain materials which will provide resistance to movement 4. What do you mean by Tension crack? (M-12) A Tension crack is a crack that develops over the top surface of a slope made of cohesion soil when slip is imminent, along which no shear resistance can develop. The depth of the tension crack is given by hc = 2c / γ, where c is the cohesion of the soil and γ is the unit weight of the soil. 5. Define critical surface of failure. (M-12) The critical surface of failure may be defined as the failure surface that has the least factor of safety against failure i.e. it is the surface along which the failure is most likely to occur. 6. What are different factors of safety used in the stability of slopes? (N-11) (a) Factor of safety with respect to cohesion (b) Factor of safety with respect to friction (c) Factor of safety with respect to shear strength (d) Factor of safety with respect to height

32 7. What is a stability number? What are the uses of stability charts? State the two basic types of failure occurring in finite slopes. (N-11) The force causing instability is the weight of the wedge which is equal to unit weight γ and the area of the wedge which is proportional to the square of the height H. Hence the weight of the wedge is proportional to γ x H 2. It is represented by Sn and is dimensionless quantity. (a) Slope failure (b) Base failure 8. What is a slide? What are the different types of Slope failure? (N-14) The failure of a mass of soil located beneath a slope is called Slide. It involves a downward and outward movement of the entire mass of soil that participates in the failure. (a) Face failure (b) Toe failure (c) Base failure 9. State some of the Slope protection measure. Slopes have been protected by adopting some successful techniques. In general, (a) Reducing the mass or loading which contributes to sliding (b) Improving the shearing strength along the anticipated zone of failure (c) Providing certain materials which will provide resistance to movement Assumptions made in stability analysis of slopes. (a) The problem is two dimensional (b) Coulomb s theory can be used to compute shear strength and shear strength is assumed as uniform along the slip surface (c) The flownet, in case of seepage, can be drawn and seepage force can be evaluated 11. Define stability number. (N 14) The force causing instability is the weight of the wedge which is equal to unit weight γ and the area of the wedge which is proportional to the square of the height H. Hence the weight of the wedge is proportional to γ x H 2. It is represented by Sn and is dimensionless quantity. 12. What are the types of slopes?

33 Slopes may be of two types, (a) Infinite slope (b) Finite slope 13. What are the types and causes for slope failure? a) Face failure b) Toe failure c) Base failure Failure of slope may occur due to, (a) The action of gravitational forces (b) Seepage forces within the soil (c) Due to excavation or undercutting of its foot (d) Due to gradual disintegration of the structure of the soil 14. What are the various methods of analysis of finite slopes? (a) Culmann s method of planer failure surface (b) The Swedish circle method or Slip circle method (c) The friction circle method (d) Bishop s method 15. Define factor of safety and critical depth. The ratio of the shearing resistance available along a slip surface to the total mobilized shearing resistance is called factor safety. It is given by, The depth H, at which the shear stress on the slip plane equals the shear strength of the soil is referred to as the critical depth Hc. 16. How does tension crack influence stability analysis? If a tension crack of depth, develops, water will enter in the crack, exerting a hydrostatic pressure force Pw acting at a height, thereby making the portion ineffective in resisting the slide.

34 17. Write the equation for factor safety derived in Swedish circle method for cohesive soil against sliding. 18. What are the 3 forces acting in circular failure while analyses through friction circle method? (a) Weight (w) of the sliding wedge (b) Cohesive force (C) developed along the slip surface (c) Reaction (R) on the slip surface 19. What are the types of movement related to landslide? (a) Creep (b) Pre-failure movements (c) Movements during slide (d) Post-failure movements 20. Explain the aspects of slope stability analysis. (a) Finding the most severely stressed internal surface and the associated shearing stress (mobilized shear strength) along the surface and (b) Finding the shear strength along the above surface 21. When does the stability analysis required in earth structure construction. (a) During construction (b) At the end of construction (c) During the working stage (d) Under long-term condition 22. A slope is to be constructed at an inclination of 30 0 with the horizontal. Determine the safe height of the slope at factor of safety of 1.5. The soil has the following properties, c = 15kN/m 2, ϕ = and γ = 19kN/m 3. (N-10) Solution: The mobilised frictional angle ϕm is given by,

35 23. Find the factor of safety of an infinite slope having a slope angle of The slope consists of cohesionless soil with angle of internal friction Given: ϕ = 36 0 ; i = 30 0 ; Solution:

36 PART B (16 Marks) 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. (M-10) 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 19kN/m 3. (M-10) 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/m 2 ; Φ = 15 ; e = 0.8 and G = 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? (N-12) 4. Write down the procedure for determining the factor of safety of a given slope by friction circle method. (N-12) 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/m 2, Φ = 20, e = 0.9 and G = 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. (M-12) 7. What are different types of slope failures? Discuss the various methods for improving the stability of slopes. (N-11) 8. An embankment 10 m high is inclined at 35 to the horizontal. A stability analysis by the method of slices gave the following forces: ΣN = 900kN, ΣT = 420kN, ΣU = 200kN. If the length of the failure arc is 23.0 m, find the factor of safety. The soil has c = 20kN /m2 and Φ = 15 o. (N-11) 9. Explain the Swedish slip circle method in detail. (M-11) 10. Explain Taylor s stability number and its applicability. (M-11) 11. Explain in detail the friction circle method of stability analysis for slopes with sketch. (M-11)