Basics of GEOTECHNICAL ENGINEERING
DEFINITION OF SOIL
- According to Terzaghi’s equation
For engineering purpose, Soil is defined as natural aggregate of mineral grains, loose or moderately cohesive, inorganic or organic in nature.
- According to Geologist
Soil is defined as disintegrated rock.
- According to Agriculturist
Soil is loose mantle at the surface of the earth which famous the growth of plant.
- RESIDUAL SOIL
The residual soils are formed by weathering of rocks, but located at the place of origin.
These soils are formed from rocks like granite, basalt, sandstone salts.
Sand, silt and clays are residual soils.
- TRANSPORTED SOIL
Those soils which are carried away by the force of wind, ice, water and gravity.
Cohesionless soils are formed due to physical disintegration.
Soil transported by wind.
Soil transported by running water.
Soil which is deposited at the bottom of the lakes.
Soil transported by gravitational force.
Also known as Glacier Soil or Simple Drift
Soil transported by glaciers either by ice or by water issuing from melting of glaciers.
- CUMULOSE SOIL
The accumulation of decaying and chemically deposited vegetable matter under conditions of excessive moisture results in the formation of this type of soil.
Ex.- Peat and Muck.
Property of soil which allows it to be deformed rapidly without rupture, without elastic rebound and without volume changes.
IS plasticity chart is plot of Ip vs WL.
- PLASTIC LIMIT
Minimum water content at which a soil will just begin to crumble when rolled into a thread approximately 3 mm in diameter.
It exists in Clays.
- LIQUID LIMIT
Minimum water content at which the soil is sufficiently fluid to flow a specified amount when jarred 25 times in standard apparatus.
Water content in a soil at which just shear strength develops is called Liquid Limit.
It exists in Clays.
In Liquid limit test, Height of fall of cup = 1 cm.
Determination of liquid limit in lab., soil sample passing through 425 μ sieve is used.
As per IS, Liquid limit lie between 35% to 50%, then soil is classified as Soil with Medium compressibility.
The capacity of soil to resist shearing stresses is known as Cohesion.
When sensitive clays are used in construction, they lose strength due to remoulding during construction operations, with the passage of time the strength again increase though not to the same original level. This phenomenon of ‘strength lose and
strength gain’ with no change in volume or water content is called Thixotrophy.
When compressive load is applied to soil mass, a decrease in its volume takes place. The property of soil mass pertaining to its susceptibility to decrease in volume under pressure is called Compressibility.
Every process involving decrease in the water content of saturated soil without replacement of the water by air is called Process of Consolidation.
In coarse grained sand having high permeability and low plasticity, 95% of consolidation occurs within 1 min of application of load.
Opposite of consolidation.
Process involves an increase in water content due to an increase in the volume of voids.
Montmorillonite clay mineral gives maximum swelling.
- WATER CONTENT (w)
Ratio of weight of water to the weight of solids.
Expressed in Percentage (%).
Water content = w = Ww/Ws x 100.
DENSITY OF SOIL
Bulk Density (ρ)
Ratio of total mass of soil to the total volume of soil.
Expressed in kg/m3.
Bulk density = ρ = M/V
Bulk density of cohesionless soil determined by Sand Replacement Method.
Bulk density of cohesive soil determined by Core Cutter method.
Dry Density (ρd)
Ratio of mass of solids to total volume of the soil in moist condition.
Dry density = ρd = Ms/V
Density of solids (ρs)
Ratio of mass of solids to volume of solids.
Density of solids = ρs = Ms/Vs
Saturated Density (ρsat)
Soil mass is saturated, its bulk density is saturated density.
Saturated density = ρsat = Msat/V
Submerged or Buoyant Density (ρsub)
Ratio of submerged mass of soil solids to total volume of the soil.
Submerged density = ρsub = Ms (sub)/V
- UNIT WEIGHT OF SOIL
Expressed in N/m3 or kN/m3.
Unit weight of water = 9.81 kN/m3.
Bulk Unit Weight or Moist Unit Weight of soil (γ)
Ratio of total weight of soil to total volume of soil.
Bulk unit weight of soil = γ = W/V
Dry Unit Weight of soil (γd)
Ratio of weight of solids to total volume of soil.
Dry unit weight of soil = γd = Ws/V
Unit Weight of Solids (γs)
Ratio of weight of solids to volume of solids.
Unit weight of solids = γs = Ws/Vs
Saturated Unit Weight of soil(γsat)
Ratio of saturated unit weight of soil to total volume of soil.
Saturated unit weight of soil = γsat = Wsat/V
Submerged or Buoyant Unit Weight of soil (γsub)
Ratio of weight of submerged soil to total volume of soil.
Submerged unit weight of soil = γsub = Ws sub /V = γsat−γw
SPECIFIC GRAVITY (G)
Ratio of weight of given volume of solids to the weight of an equal volume of distilled water at 27℃ temperature.
G = γs/γw
For sandy soils, G = 2.7.
Weight of soil mass to the weight of an equal water = Apparent or Bulk Specific Gravity (Gm).
Gm = γ/γw
VOID RATIO (e)
Void ratio = Total volume of voids/Volume of soil solids = Vv/Vs
Void ratio for sandy soil = 0.6.
Void ratio always lies from 0 to 1.
Porosity = Total volume of voids/Total volume of soil mass = Vv/V
DEGREE OF SATURATION (Sr)
Sr = Volume of water in soil mass/Total volume of the voids = Vw/Vv
For the moist soil, Sr = 50 to 75%.
For Fully saturated soil, Sr = 1.
For perfectly dry soil, Sr = 0.
PERCENTAGE AIR VOIDS (na)
Ratio of volume of air voids to the total volume of the soil mass.
Expressed in Percentage (%).
na = Va/V x 100
AIR CONTENT (ac)
Air content = ac = Volume of air voids/Volume of voids
Air content = ac = 1 – Sr
DENSITY INDEX (ID)
Also known as Relative Density or Degree of Density.
Ratio of difference between the void ratio of the soil in its loosest state (emax) and its natural voids ratio (e) to difference between the void ratio in the loosest (emax) and densest state (emin).
ID = emax− e/emax− emin
ID varies from 0 to 1 or 0 to 100%.
e = n/1−n
n = e/1+e
G.w = e.Sr
γd = γ/(1+w)
γd = G γw/(1+e)
γd = G γw(1 – n)
γsat = (G+e) γw/(1+e)
γsat = G γw(1 – n) + n γw
γsub = (G−1) γw/(1+e)
ac = 1 – Sr
DETERMINATION OF WATER CONTENT
Oven Drying Method
Most accurate method.
Sample is kept at temperature of 105℃ to 110℃ for 24 hours.
Sand Replacement Method
Used when oven drying method is not available.
Calcium Carbide Method
Especially suited where water content is quickly determined for the purpose of field content like, compaction of an embankment.
Quick method of determining whose specific gravity is accurately known.
Suitable only for coarse grained soils.
DETERMINATION OF SPECIFIC GRAVITY
Density Bottle Method
This method is accurate & suitable for all type of soil.
Used only for coarse grained soil.
DETERMINATION OF PARTICLE SIZE DISTRIBUTION
Shape of particle size curve represented by Cc.
D10 means 10% of the particles are finer than this size.
D10 is Effective size or Effective diameter.
Uniformity coefficient = D60D10
Particle size range is measured by Uniformity coefficient.
For uniformly graded soil, Uniformity coefficient = 1.
For well graded soil, Uniformity coefficient = more than 10.
Two methods for particle size distribution: 1. Sieve Analysis & 2. . Sedimentation Analysis.
75 μ(micron) is smallest sieve used in sieve analysis.
Based on Stroke’s Law.
Upper limit of particle size for the validity of the stock’s law is 0.2 mm and lower limit 0.0002 mm.
Analysis done by the help of Hydrometer or Pipette.
Used to determine the density of soil suspension.
Hydrometers are calibrated at 27℃.
When this analysis performed, it require correction for temperature,
meniscus (hydrometer reading) & dispersing agent only.
This analysis is Standard sedimentation method used in the laboratory.
Determination of size of particle consists of 7 g sodium carbonate, 33 g sodium hexameta phosphate and 1 litre distilled water.
DETERMINATION OF CONSISTANCY OF SOIL
Consistency denotes degree of firmness of soil.
Shrinkage limit :- Maximum water content of saturated soil at which a reduction in its moisture does not cause a decrease in volume of the soil mass.
At shrinkage limit, the soil is saturated.
Four states of consistency: Solid state, Semi-solid State, Liquid state & Plastic State.
Solid state :- When water content in a soil is reduced beyond the shrinkage limit, the soil will be in Solid state.
Liquid state :- The minimum water content at which the soil is still in the liquid state and just develops the shear strength against flowing.
Plastic state :- The minimum water content which makes the soil to be rolled into 3 mm diameter threads.
PLASTICITY INDEX (Ip)
Difference between liquid limit and plastic limit.
When wP is equal or greater than wL, then Ip is zero.
As per Atterberg, Ip < 7 then soil is low plastic.
As per Atterberg, Ip > 17 then soil is highly plastic.
SHRINKAGE INDEX Is
Difference between liquid limit and shrinkage limit.
CONSISTENCY INDEX or RELATIVE CONSISTANCY(Ic)
Ratio of liquid limit minus natural water content to plasticity index.
Ic = wL− w/Ip
If Ic = 0 for soil, its Liquid Limit.
If Ic = 1 for soil, its Plastic Limit.
If Ic > 1 for soil, its Semi-solid State.
LIQUIDITY INDEX IL
Ratio of water content minus its plastic limit to the plasticity index.
IL = w – wp/Ip
Soil is at Liquid Limit, IL = 1.
Soil is at Plastic Limit, IL = 0.
IL + Ic = 0.
Flow Index :- It indicates the shear strength variation with water content in soils.
Toughness Index :- Plasticity Index/Flow Index
ACTIVITY OF CLAY
Activity of Clay = Plasticity Index/Clay Friction
Clays which exhibits high activity contain montmorillonite & have high plasticity index.
SENSITIVITY OF CLAY
Sensitivity = Unconfined Compressive Strength of natural or undisturbed / Unconfined Compressive Strength of soil in remoulded state without
Sensitivity of most clays = 1 to 8.
For Normal clays = 2 to 4.
Unconfined Compressive Strength of very soft clay = 10 to 25 kN/m2 & for hard clay = above 400 kN/m2.
- Single Grained Structure
This arrangement composed of individual soil particles.
This structure found in Coarse Grained Soils.
- Honey Combed Structure
Arrangement of soil particles having a comparatively loose, stable structure resembling a honey comb.
Observed in silty soils & fine grained soils.
- Flocculent Structure
Arrangement composed of flocs of soil particles instead of individual soil particles.
The particles of soil are oriented ‘Edge to Edge’ or ‘Edge to Face’ respect to one another.
Observed in Clay deposits & fine grained soil.
- Dispersed Structure
Arrangement composed of particles having ‘face to face’ or parallel orientation.
Observed in fine grained soils.
- Coarse-grained Skeleton Structure
Arrangement of coarse grains forming a skeleton with its interstices partly filled by a relatively loose aggregation of the finest soil grains.
Observed in Composite soils.
- Cohesive Matrix Structure
Arrangement in which a particle to particle contact of coarse fraction is not possible.
Observed in Composite soils.
The property of soil mass which permits the seepage of water through its interconnecting voids is called Permeability.
A soil having continuous voids is called Permeable soil.
Gravel is highly permeable soil.
Stiff clay is least permeable soil. (But clay is termed as impermeable for all practical purpose.)
Hydraulic Gradient:- The loss of head or dissipation of the hydraulic head per unit distance of flow through the soil is called H.G.
Darcy give relation for saturated soil that ‘the rate of flow or discharge per unit time is proportional to the hydraulic gradient’.
Permeability determined by Falling head & Constant head permeameter (used for coarse grained soil).
Value of permeability depends upon the direction of flow of water through the soil mass.
Permeability directly proportional to the square of average size particle & inversely proportional to the viscosity.
Coefficient of Permeability
The average velocity of flow that take place through total cross sectional area of soil under unit hydraulic gradient is known as Coefficient of Permeability.
Unit of Coefficient of Permeability is m/s.
Quantity of seepage of water in soil medium directly proportional to the co-efficient of permeability.
Coefficient of permeability increase with increase in temperature.
Coefficient of permeability of Silt is less than that of Clay.
The pressure exerted by water on the soil through which it percolates is known as Seepage Pressure.
It’s very important in the stability analysis of earth structure subjected to the action of seepage.
Seepage Pressure always acts in the direction of flow.
If Seepage Pressure acts in downward direction, effective pressure is increased.
If Seepage Pressure acts in upward direction, effective pressure decreased.
Seepage Pressure is independent of the coefficient of permeability.
Seepage Force in soil proportional to the Head Loss & Exit Gradient.
Seepage Force is perpendicular to equipotential line.
If seepage pressure becomes equal to the submerged weight of the soil, the effective
pressure reduced to zero. In that case, cohesionless soil losses all shear strength and soil particles have tendency to move up in direction of flow. This phenomenon of lifting soil particles is called Quick Sand Condition.
The hydraulic gradient at which quick sand condition occurs is called Critical Hydraulic Gradient ic .
H.G. = ic = (G−1)/(1+e)
H.G for all soils = Unity.
H.G increase with increase in specific gravity of the soil and decrease in void ratio.
Flow net is used to determine the seepage flow, hydrostatic pressure, seepage pressure, exit gradient.
Flow net is network of flow line and equipotential line.
Also known as Stream Line.
Flow line in seepage through soil medium is defined as the path of particles of water through a saturated soil mass.
Eq. line in a seepage through soil mass is defined as the line connecting the points of equal head of water.
Upstream slope of an earth dam under steady seepage condition is called Equipotential line.
The direction of seepage is always perpendicular to the equipotential line.
Flow lines & Eq. lines are intersecting lines at 90° to each other.
The portion between any two successive flow lines is known as Flow Channels.
The portion enclosed between two successive equipotential lines and successive flows lines is known as Field.
Also known as Downstream Gradient or Tail water Gradient.
The hydraulic gradient provided at the downstream side of a hydraulic structure such as dam is called Exit Gradient.
Exit Gradient = Head Loss/ Length of Seepage
Maximum permissible exit gradient is the critical gradient divided by factor of safety.
STRESS CONDITION IN SOIL
Total stress at any plane in a soil mass is the total load per unit area.
Total stress consists of effective stress and neutral stress or pore water pressure.
Effective stress on the soil is due to external load acting on the soil and self-weight of the soil particles.
This stress is effective in decreasing the void ratio of the mass and in mobilising its shear strength.
Effective stress is increased if the water is flowing from upward on the soil mass.
Decrease in effective stress accompanied by increase in neutral stress.
Neutral Stress or Pore Water Pressure
Neutral stress on the soil is due to weight of water present in soil pores.
It is transmitted to the soil base through the pore water.
This stress does not have any measurable influence on the void ratio or any mechanical property.
Neutral stress is decreased if the water is flowing from downward on the soil mass.
COEFFICIENT OF COMPRESSIBILITY av
Decrease in void ratio per unit increase in pressure is called av.
Unit of av is inverse of pressure.
If pressure on clay layer increase from p to p + δp and void ratio decrease from e0 to e then, av = e0− e/ δp
The value of av decrease with increase in pressure.
COEFFICIENT OF VOLUME COMPRESSIBILITY mv
Change in volume of soil per unit of initial volume due to given increase in the pressure is called mv.
mv = av/1+ e0
mv directly proportional to av.
mv decrease with increase in pressure and void ratio.
COEFFICIENT OF CONSOLIDATION Cv
Cv adopted to indicate the combined effects of permeability and compressibility of soil on the rate of volume change.
Cv is used for evaluating time rate of settlement.
Cv = k/mvγw where, k = coefficient of permeability
Unit of Cv = cm2/s.
Rate of consolidation increase with increase in temperature.
In consolidation testing, curve fitting method is used to determine Coefficient of Consolidation.
DEGREE OF CONSOLIDATION (U)
Downward movement of the surface of a consolidating layer at any time during process of consolidation is called Consolidation Settlement.
Ratio of settlement of fully thickness of the clay to the ultimate or final settlement when the process of consolidation is complete, is known as Degree of Consolidation.
Expressed as Percentage.
U is function of Time Factor Tv .
Tv = Cv t/d2
Where, d = Drainage path = The maximum distance which the layer particles have to travel for reaching the free drainage layer.
Time factor for clay layer is directly proportional to permeability.
Time factor corresponding to 25% degree of consolidation is given by π/64
Time(t) required to attain certain degree of consolidation is directly proportional to the square of drainage path and inversely proportional to the coefficient of consolidation.
U or time factor depends upon
Thickness of clay layer
Number of drainage faces
Coefficient of permeability
Coefficient of consolidation
Magnitude of consolidating pressure
SHEAR STRENGTH OF SOIL
Shear strength of soil identified by Ultimate Shear Stress.
The shear strength of soil is the resistance to deformation by continuous shear displacement of soil particles due to the action of shear stress.
Vane shear test & Triaxial compression test used to determine Shear strength of soil.
Shear strength of soil is due to
1. Structural resistance
2. Frictional resistance
The structural arrangement of soil particles affects the shear stress because of the interlocking of the particles.
The same soil exhibit different shear strength at different void ratio and also at different rate of loading.
The internal friction between soil particles resists the shearing friction of soil mass.
Frictional resistance of clayey soil is less than sandy soil.
Important property for fine grained soils.
Coarse grained soil do not exhibits any cohesion.
Shear strength in cohesionless soil results from inter granular friction alone, while in all other soils it result from both cohesion & friction.
ANGLE OF INTERNAL FRICTION
Also known as Angle of Shearing Resistance.
The measure of the shearing resistance of soil to sliding along a plane is termed as ∅.
It depends upon the shape of the particles, surface roughness, type of interlocking, lateral pressure and the state of packing.
∅ varies with normal direct pressure and the density of sand.
∅ of round grained loose sand = 25° to 30°.
∅ of dense sand = 32° to 37°.
- COULOMB’S LAW
“The shearing strength of soil consists of cohesion and friction between soil particles.”
τ = C + σ tan ∅
τ for sand = σtan ∅.
τ for cohesive soil = C.
- EARTH PRESSURE
A structure used for maintaining the ground surfaces at different elevations on either side of it is called Retaining Wall.
Critical height for stability of soil is the maximum height at which it is possible for the sloped bank of soil to be stable.
The material retained or supported by the structure = Back fill.
If the position of the backfill lies above the horizontal plane at the elevation of the top of the structure = Surcharge.
Inclination of the surcharge to the horizontal = Surcharge angle.
Lateral pressure exerted by the soil when the retaining wall has no movement relative to the backfill = Earth pressure at rest.
Earth pressure at rest can be determined by using the theory of elasticity assuming the soil to be semi-infinite, homogeneous, elastic and isotropic.
Earth pressure may be Active or Passive earth pressure.
Active Earth Pressure
Lateral pressure exerted by the soil when the retaining wall tends to move away from the backfill due to excessive pressure of the retained soil is called A.E.P.
Its the minimum pressure exerted by soil on the retaining wall.
Active earth pressure ∝ cot2 45°+∅2
Effect of cohesion is to decrease the active earth pressure all along the height of a retaining wall.
Passive Earth Pressure
Lateral pressure exerted by the soil when the retaining wall moves towards the
backfill due to any natural cause is called P.E.P.
Maximum pressure due to maximum shear stress on the retaining wall.
Passive earth pressure ∝ tan2 (45°+∅/2)
The value of earth pressure at rest is higher than active earth pressure but less than passive earth pressure.
COEFFICIENT OF EARTH PRESSURE (k)
Ratio of horizontal stress σh to vertical stress σv = k.
The coefficient of active earth pressure = ka = (1− sin∅)/(1+ sin∅)
The coefficient of passive earth pressure = kp = (1+ sin∅)/(1− sin∅)
ka is always less as compared to kp.
When soil is at elastic equilibrium, coefficient of earth pressure at rest, ko = μ/(1− μ )
ko for loose sand = 0.4
ko for hard clay = 0.5
ko for soft clay = 0.6
ko for dense sand = 0.6
ko for stiff clay or sand compacted in layer = 0.8
- BEARING CAPACITY OF SOIL
The load or pressure developed under the foundation without introducing any
damaging movement in the foundation and in the supporting structure = S.B.C.
Depends upon grain size of the soil, size and shape of footing.
Bearing capacity of soil increase with decrease in area of the footing.
Bearing capacity factor Nc, Nq & Nr is function of internal friction angle.
- ULTIMATE BEARING CAPACITY
Total pressure at the base of the footing due to the weight of superstructure, self-weight of footing & weight of the earth fill is called Gross pressure intensity.
Difference between intensities of the gross pressure due to construction of the structure and original overburden pressure is called Net pressure intensity.
Minimum gross pressure intensity at the base of the foundation at which the soil fails in shear is called Ultimate Bearing Capacity.
Minimum net pressure intensity at the base of the foundation at which soils fails in shear is called Net Ultimate Bearing Capacity.
Net Safe Bearing Capacity = Net Ultimate Bearing Capacity /Factor of Safety
Maximum pressure which the soil can carry without any risk of shear failure is called Safe Bearing Capacity.
Net loading intensity at which neither the soils fails in shear nor there is excessive settlement detrimental to the structure is called Allowable Bearing Capacity.
Chemical Weathering of soil is caused due to Oxidation, Hydration, Carbonation and Leaching.
Mechanical Weathering of soils is caused due to Periodical temperature changes, Splitting action of ice and Splitting action of flowing water.
Black Cotton Soil is inorganic in nature, contains large percentage of clay mineral & exhibit high compressibility and Expensive soil.
Dilatancy :- Expansion of soil due to shear at constant value of pressure is called Dilatancy.
Piping failure in a hydraulic structure can be prevented by
Diverting the seepage water into filter wells
Increasing the creep length of flow of water
Increasing the stress due to weight of the structure.
Critical Density :- Density of sand at which there is no change in volume under the influence of shearing strain produced due to shear stress is called Critical Density.
Saturation Line :- A line showing the dry density as a function of water content for soil containing no air voids is called Saturation Line.
A portion of the foundation of structure which transmits the load directly to the soil is called Footing.
Settlement of footing in sand depends upon
- Stress deformation characteristics of sand
- Relative density of sand
- Width of footing
Contact pressure of flexible footing on non-cohesive soil is More in centre than at the edges.
Contact pressure of rigid footing on cohesive soils is less in centre than at the edges.
Soil Compaction :- Process of obtaining increased density of soil in a fill by reduction of its pore space by the explusion of air is known as Soil Compaction.
Soil Stabilisation :- Process of maintaining or improving the performance of soil as a constructional material usually by the use of admixture is known as Soil Stabilisation.
As per IS soil classification, SM soil is designed as Silty Sand & M soil is designed as Silt.
Montmorillonite is primary constitute for Black Cotton Soil.
Kaolinite is primary constitute for China Clay.
Held water in soil is known as Structural water, Capillary water, Adsorbed water & Hygroscopic water.
Clay particles carry Negative Charges on their faces.
When drainage is permitted throughout the triaxial test, then it called Drained test.
For Stabilization of heavy clays, chemical stabilization is most effective.
Smooth Wheeled Roller = Suitable for compaction Cohesionless soil.
Pneumatic Tyred Roller = Suitable for compaction of Cohesive & Cohesionless soil.
Sheep Foot Roller = Suitable for compacting Cohesive soil.
Vibroflotation Technique is best suited for coarse sand and gravel.
For Standard Proctor Test, Range of optimum water contents for clayey soil = 8 to 12%.
Soils most susceptible to liquefaction are saturated fine and medium sands of uniform particle size.
The shape of e – log p curve for soil mass gives Cc = Compression Index.
Compression Index of soil increase with increase in liquid limit.
Re-compression Index is about 1/5 of the Compression Index.
Density Index is used to estimate Angle of Internal Friction of sandy soil.
Westerguard’s analysis for stress distribution beneath loaded area is applicable to Stratified Soil.
For sampling saturated sands and other soft and wet soils satisfactorily, most suitable soil sampler = Standard Split Spoon Sampler.
Energies imparted to soil sample in modified proctor test / Energies imparted to soil sample in standard proctor test = 4.5
Shear strength test of clay cannot be done without undisturbed sampling.
Criteria for determination of allowable bearing capacity of foundation
- Shear failure
Behaviour of Sand is governed by Mass Energy.
Behaviour of Clay is governed by Surface Energy.
In Shear Box test, the failure plane is Horizontal Plane.
Common size of box in shear test = 60 x 60 x 50 mm.