Methods of Stability analysis of slope(Geotech)

Hi here is a  brief introduction to the stability analysis of the slopes.
There are following methods of stability analysis:

• (A)Slip circle method or Swedish circle method or Method of Slices:

This method assumes the surface of sliding is an arc of a circle. Soil is either purely cohesive or it will be a cohesive and frictional soil. So, analysis can be done separately as below:

• Analysis of purely cohesive soils:

An arc of a circle is assumed as the failure plane and the weight of the circular arc wedge provides a disturbing moment. This disturbing moment is stabilized by the stabilizing moment developed due to the presence of the cohesion along the arc surface.
These two moments are equated to get the limiting values. The ratio of the resisting moment to the stabilizing moment gives us the Factor of safety.

• Cohesive and frictional soils:

In such soil again a circular arc is assumed to be a failure wedge and the weight of the wedge is resolved into tangential and normal directions. The tangential weight will provide us with the disturbing moment about the center of rotation and the normal force will provide us the frictional resistance which along with the cohesion force will produce the stabilizing moment.

• (B) Friction circle method

This method is applicable to cohesive as well as frictional soils and assumes the failure surface as an arc of a circle.  There is a small circle known as friction circle. 

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Stability of Earth Dam (slope)

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Earth dams must be safe against slope and foundation failure for all operating conditions. There are three generally recognized critical stages based on pore pressure condition for which the stability of the embankment should be ascertained. These three situations are

• End of construction
• Steady state seepage
• rapid state seepage.

Usually construction pore pressure reach their maximum value when the embankment reaches maximum height. After the reservoir has been filled for a long time, pore pressures are determined by steady-stage seepage conditions and may be estimated by the construction of flow net.

Rapid lowering of the reservoir produces the third critical situation, particularly for low permeable soils. Upstream slope stability may be critical for the construction or rapid draw-down condition. The downstream slope should be checked for the construction and steady-seepage condition.

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Reference: G K Publishers - GATE 2013

GATE, PSUs preparation- Soil Engineering ( notes)- Part 11

Hello there,
Welcome to the part 11 of the one liner notes useful for the preparation of GATE and other similar examinations.

1. For compaction of cohesion-less soils vibration techniques, flooding the soil and heavy weights dropping from a height are most suitable methods.
2. Standard split spoon sampler is most suitable soil sampler for saturated sands and other soft and wet soils.
3. Raft are used when structural load is uniform and soil is soft clay, made up of marshy land.
4. Piles are used when structural load is heavy and/or soil is having low bearing capacity for a considerable depth.
5. Footings are used when soil is having good bearing capacity at shallow depth and structural load is within permissible limit.
6. Well or pier is used when structural load of bridge is to be transferred through sandy soil to bed rock.
7. At critical void ratio, the void ratio does not vary with shear strain.
8. Vane shear test is performed on soft clay.
9. Standard penetration test is performed on sandy deposits.
10. Static cone penetration test is useful for end bearing and skin friction resistance determination.
11. Pressure meter test is useful for In-situ stress strain characteristics.
12. Differential settlement of foundation is hazardous because it leads to damage to superstructure.
13. Lowering of ground water table can cause settlement of foundation.
14. Consolidation and unconfined compression tests require undisturbed samples.
15. Clays which exhibit high activity contains montmorillonite and have a low plasticity index.
16. Size ranges of voids in soil also effect the permeability.
17. During seepage through an earth mass, the direction of seepage is perpendicular to the equipotential lines.
18. Limitation of direct shear test are plane of failure is predetermined, no control over drainage and there is non-uniform distribution of stresses.
19. Coulomb's theory assumes that failure occurs on a plane surface and failure wedge is a rigid body.

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GATE, PSUs preparation- Soil Engineering ( notes)- Part 10

Hello there,
Welcome to the part 10 of the one liner notes useful for the preparation of GATE and other similar examinations.

• Allowable bearing pressure is the net loading intensity at which neither soil fails in shear nor is there any excessive settlement.
• Ultimate bearing capacity is the minimum gross pressure intensity at the base of foundation at which soil fails in shear.
• Net safe bearing capacity is defined as the net ultimate bearing capacity divided by factor of safety.
• Safe bearing capacity is the maximum pressure which soil can carry safely without risk of shear failure.
• The concept of useful width is used to determine ultimate bearing capacity of an eccentrically loaded square footing.
• Pressure distribution in pure clayey soil subjected to a uniformly distributed load(udl) through a rigid footing  is parabolic with minimum at the center and maximum at the outer edges, but it becomes maximum at the center and minimum at the edges when udl is transmitted through rigid footing placed on the surface of a cohesion less soil.
• The ultimate bearing capacity of a pile is given by (9.Cu.Ab + a.Cu1.As), where 'Cu' is the given cohesion, 'Cu1' is the average coheasion and 'a' is adhesion factor given by Cu1/2. 
• The upstream slope of an earth dam under steady seepage condition is equipotential line.
• In tri-axial test intermediate and minor principal stresses are equal, volume changes can be measured and field conditions can be stimulated.
• Active earth pressure occurs when wall moves away from backfill, passive earth pressure occurs when wall moves towards the back-fill and earth pressure at rest occurs when the wall is at rest.

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GATE, PSUs preparation- Soil Engineering ( notes)- Part 9

Hello there,
Welcome to the part 9 of the one liner notes useful for the preparation of GATE and other similar examinations.

• A shallow foundation is defined as a foundation which has a depth of embedment less than its width.
• For sand of uniform spherical particles, the ratio of void ratios in the loosest and the densest states is 2.6.
• The description of 'sandy silt clay' signifies that the soil contains unequal proportions of the three constituents such that clay>silt>sand.
• A soil having particles of nearly the same size is known as uniformly graded.
• The soils most susceptible to liquefaction are saturated fine and medium sands of uniform particle size.
• The value of bearing capacity factor for cohesion Nc, for piles as per Meyerhof is taken as 9.0.
• The slope of the e - log p curve for a soil mass gives compression index, Cc.
• Degree of freedom of a block type machine foundation is 6.
• Given that damping ratio = 0.10 and damping coefficient = 225 kN sec/m. The the critical damping coefficient in kN sec/m will be 2250.
• The natural frequency of a vibrating foundation system increases as the square root of the spring stiffness and decreases with the square root of the mass of the body.
• Terzaghi's equation of ultimate bearing capacity for a strip footing may be used for square footing resting on pure clay soil with the correction factor 1.3.

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GATE, PSUs preparation- Soil Engineering ( notes)- Part 8

Hello there,
Welcome to the part 8 of the one liner notes useful for the preparation of GATE and other similar examinations.

• According to Terzaghi's theory, the ultimate bearing capacity at ground surface for a purely cohesive soil and for a smooth base of a strip footing is 5.14.C where, C = unit cohesion of soil.
• The net ultimate bearing capacity of a purely cohesive soil is independent of both depth and width of footing.
• The rise of water table below the foundation influences the bearing capacity of soil mainly by reducing cohesion and effective unit weight of soil.
• Terzaghi's general bearing capacity formula for a strip footing gives us the ultimate bearing capacity of soil. Formula uses three bearing capacity factor.
• Terzaghi's bearing capacity factors are the functions of angle of internal friction only.
• In the plate load test for determining the bearing capacity of soil, the size of square bearing plate should be between 300 mm and 750 mm.
• Bearing capacity of soil depends upon type of soil, shape and size of footing and is independent of rate of loading.
• Rise of water table up to ground surface reduces the net ultimate bearing capacity of soil  approximately by 50%.
• Contact pressure beneath a rigid footing resting on cohesive soil is more at edges compared to middle.
• According to IS specifications, the minimum depths of foundation in sand and clay should be respectively 800 mm and 900 mm.
• The maximum differential settlement in isolated footings on clayey soils should be limited to 40 mm.
• A combined footing is generally used when number of columns is two and they are spaced close to each other.
• Negative skin friction on a pile acts downwards and reduces the load carrying capacity of the pile.
• Generally the bearing capacity of a pile group is equal to the sum of bearing capacities of individual piles in case of end bearing piles.
•  The settlement of a group of friction piles as compared to that of a single pile is more.
• Negative skin friction is caused by relative settlement of soil and skin frictional resistance is caused by relative settlement of pile.
• Static formulas are suitable for friction piles driven through cohesive soils.
• Dynamic formulas are suitable for friction piles driven through cohesion-less soils.
• Dynamic formulas do not take into account the reduced bearing capacity of a pile in a group.
• Mechanical stabilization of soil is done with the help of proper grading.
• Lime stabilization is very effective in treating plastic clayey soils.
• Undisturbed samples are obtained by thin-walled samplers.
• Stationary piston sampler and rotary sampler are both thin-walled sampler.
• Greater skin friction retards the sinking of the well.
• If the bearing capacity of a footing on a saturated clay is 120 kN/m2 , the bearing capacity of a circular footing(diameter=width) will be more than 120 kN/m2.
• A plate load test is useful to estimate both bearing capacity and settlement of foundation.

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GATE, PSUs preparation- Soil Engineering ( notes)- Part 7

Hello there,
Welcome to the part 7 of the one liner notes useful for the preparation of GATE and other similar examinations.

• In a triaxial compression test when drainage is allowed during the first stage(i.e. application of cell pressure) only and not during the second stage (i.e. application of deviator stress at constant cell pressure), the test is known as consolidated undrained test.
• When a sample of sand is sheared under undrained condition, then volume of sample does not change.
• The ratio of the undisturbed shear strength to the remoulded shear strength in the cohesive soils under undrained conditions is greater than 1.
• Sensitivity of a soil can be defined as ratio of compressive strength of unconfined undisturbed soil to that of soil in a remoulded state.
• Rankine's theory of earth pressure assumes that the back of the wall is vertical and smooth.
• The major principal stress in an element of cohesion-less soil within the backfill of a retaining wall is vertical if the soil is in an active state of plastic equilibrium.
• The effect of cohesion on a soil is to reduce the active earth pressure intensity but to increase the passive earth pressure intensity.
• Co-efficient of earth pressure at rest is greater than the active earth pressure but less than passive earth pressure.
• Total lateral earth pressure is proportional to square of depth of soil.
• Cohesive soils are poor for back-fill because of large lateral pressure.
• Base failure of a finite slope occurs when the soil below the toe is relatively soft and weak.

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GATE, PSUs- Soil Engineering ( notes)- Part 6

Hello there,
Welcome to the part 6 of the one liner notes useful for the preparation of GATE and other similar examinations.

• In a consolidated drained test on a normally consolidated clay, the volume of the soil sample during shear decreases.
• Skempton's pore pressure co-efficient B for saturated soil is 1.
• Shear strength of a soil is a unique function of shear strength.
• In a deposit of normally consolidated clay effective stress and undrained strength increase with depth but water content decreases with depth.
• Effective angle of shearing resistance increases as the size of particles increases and is rarely more than 30 degrees for fine grained soil.
• Unconfined compressive strength test is un-drained test.
• The angle that Coulomb's failure envelope makes with horizontal is called angle of friction.
• In a tri-axial compression test on a soil specimen, the intermediate principal stress is equal to minor principal stress.
• If a cohesive soil specimen is subjected to a vertical compressive load, the inclination of the cracks to the horizontal is 45 degrees. 
• In a direct shear box test, the plane of failure is predetermined.
• Better control is achieved on the drainage of the soil in a tri-axial compression test.
• Stress distribution on the failure plane in the case of tri-axial compression test is uniform.
• If the shearing stress is zero between two planes, then the angle between the two planes is 90 degrees.
• In the tri-axial compression test, the application of additional axial stress(i.e. deviator sress) on the soil specimen produces shear stress on all planes except horizontal and vertical planes.

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You can refer such question on the book "Civil Engineering Objectives" by S P Gupta and S P Gupta.

GATE, PSUs- Soil Engineering ( notes)- Part 5

Hello there,
Welcome to the part 5 of the one liner notes useful for the preparation of GATE and other similar examinations.

• The slope of isochrone at any point at a given time indicates the rate of change of pore water pressure with depth.
• Within the consolidation process of  a saturated clay a gradual decrease in neutral pressure and a gradual increase in effective pressure takes place and sum of the two is constant.
• The value of compression index for a remoulded sample whose liquid limit is 50% is 0.28.
• Over-consolidated clay with a high over-consolidation ratio behaves like a dense sand.
• Degree of consolidation is directly proportional to time and inversely proportional to square of drainage path.
• Time factor for a clay layer is directly proportional to permeability of soil.
• If the time required for 50% consolidation of a remoulded sample of clay with single drainage is t, then the time required to consolidate the same sample of clay with double drainage is t/4.
• Co-efficient of consolidation for clay normally decrease with increase in liquid limit.
• Only in fixed ring type consolidometer, direct measurement of permeability of the specimen at any stage of loading can be made.
• Compressibility of sandy soils is much less than that of clayey soil.
• Co-efficient of compressibility of an over-consolidated clay is less than that of a normally consolidated clay.
• Co-efficient of compressibility is different for different types of soils and also different for a soil under different states of consolidation.
• The ultimate consolidation settlement of a structure resting on a soil decreases with increase in the initial voids ratio.
• The ultimate consolidation settlement of a soil is directly proportional to the compression index.
• Coarse grained soils are best compacted by a vibratory roller.
• With the increase in the amount of compaction energy optimum water content decreases but maximum dry density increases.
• The maximum dry density upto which any soil can be compacted depends upon both moisture content and amount of compaction energy.
• For better strength and stability, the fine grained soils and coarse grained soils are compacted respectively as wet of OMC and dry of OMC.
• Effective angle of internal friction for coarse grained soils is rarely below 30 degrees.
• effective cohesion of soil can have a negative value.
• Effective angle of internal friction for a soil increases as state of compactness increases.
• Effective angle of internal friction is a complicated function of mineralogy and clay size content.
• For a loose sand sample and a dense sand sample consolidated to the same effective stress ultimate strength is same but peak strength of dense sand is greater than that of loose sand.
• The shear strength of a soil increases with normal stress.

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