PROPERTIES
Father → Dr. Karl Terzaghi
Pedogenesis → Process of soil formation
Petrology → Deals with various aspects of Rocks
Soil is produced by weathering of solid rocks
Unit wt. Soil = 20kN/m^3
SSA ↑es → कोशिका वृद्धि ↑es
Sand particle → Quartz
Liquification → Loose sat sand
Dry soil is submerged under water then the soil suction is reduced.
PH soil = 5.5 - 6.5 (Slightly acidic)
PH > 11→ Salinity, practically infertile.
Soil contains hematite G = 5 -5.3
Soil particles → Vanderwalls force.
Silt → Cohesive soil.
Coefficient of Softening = Ratio of Compressive strength of material saturated with water to that in dry state
Soils containing organic matter are of spongy nature.
Dense sand & over consolidation soil → (-ve) Pore pressure
Fine grained cohesive soils → Drainage by electro osmosis
Most common medium for sediment transport → Water
Unconformity → A surface of erosion or non-deposition as detected in a sequence of rocks
Avg density of Earth = 5.51 gm/cc
Bank cubic meter → Volume of soil to be excavated in its in-place natural state
Texture of sandstone → Clastic
Moist soil is partially saturated
By appx method, the N-component at the time of sudden drawdown condition → Submerged unit weight is considered
Nuclear density Gauge → To find wet density, dry density and Moisture content
Terminal velocity → Maximum constant velocity with which body will fall in fluid medium
Sodium chloride is used in soil to get a Dense hard mat with stabilised surface after crystallisation occurs in the pores of soil
Soil formation
Geological Cycle : Weathering → transportation → deposition → upheaval → weathering & Repeat.
Physical weathering/disintegration → Cohesionless soils
Chemical weathering/disintegration → Clay & Silt
Water
Hydroscopic water → Driven off by heat
Hygroscopic water → Absorbed by the particles of dry soil from the atmosphere
Structural water → Chemically combined in the crystal str of the soil mineral and can be remove only by breaking the crystal str
Adsorbed water → Water held by electro-chemical forces existing on soil surface, affects physical properties of fine-grained soil, allows clay particle to deform plasticity, has little effect on properties of coarse-grained soils
Plastic characteristics of clays are due to → Adsorbed water
Gravitational water → Can be removed from soils by drainage
Capillary water → Held above water table by surface tension
Solvate water → Forms hydration shell around soil grains
Field capacity → Maximum amount of water that soil can hold by capillary action
Types Of Soil
Residual Soil → Bentonite
Alluvial → River deposit, dark in colour, ex. Gravel & Sand.
Lacustrine → by Lake, ex.
Aeoline → By wind, ex. Loess,
Glacial soil → Till, Drift, glacier deposit
Gravity deposit → Colluvial or talus, found in valleys.
Gumbo soil → Black coloured soil, which is sticky & highly plastic in nature.
Black cotton soil → Cohesive soil, High plasticity & low shearing strength , more swelling & shrinkage due to montmorillonite, Expansive in nature due to silica, Decomposition of Basalt, Southern India.
Loess → wind blown, collapsible, (0.01mm - 0.5mm), yellowish or pallor colour, low density & high compressibility.
Loam (Garden soil) → mix of sand + silt + clay, best for plant growth & garden, Suitable for construction material
Bentonite → a clay ,formed from volcanic ash by chemical action,used as lubricant & in drilling operations.
Organic soil → Muck, Peat & Humus
Peat → Organic soil, wind blown
Muck or peat → swamp & marsh deposit
Laterite (lateritic soil) → Decomposition of rocks,removal of bases & silica & accumulation of iron oxide & Aluminum oxide
Incoherent alluvium → Soil composed of loose granular graded material which can be scoured off with the same ease with which it is deposited.
Varved clays → Sedimentary deposits consisting of alternate thin layers of silt and clays.
Oolitic sand → Rounded, Biogenetic sand → Cemented, Calcareous Clay → Crushing, Soft clay → Under-consolidated
Drilling mud → Mixture of Bentonite clay + Water
Alkali soil → electrical conductivity < 4000 micro-ohms/cm, pH = 8.5 - 10.0, exchangeable sodium content > 15.
Water content
w = Ww/Ws = Mw/Ms = water/solid
w ≥ 0
Ws = W/(1+w)
★ Bulking = extra depth / actual depth = D1-D2/D2 = water content
Void Ratio
e = Vv/Vs = η/(1-η)
Range 0 < e < ∞
sandy soil e = 0.3
emax = 0.91 (for Sandy soil Spherical in shape & Uniform in size)
emin = 0.35
emax/emin = 2.6
if e = constant → γd = constant
e dry state = e saturation state.
Porosity
η = Vv/Vttl = e/(1+e)
Range 0 < η < 1
compacted sand η = 30-40%
loose soils η = 50-60%.
e = n/1-n
η = e/1+e
Degree of saturation
S = Vw/Vv = 1 - αc
air content
αc = Va/Vv = 1 - S
αc + S =1
% air void
ηa = Va/V
ηa = η.αc
Density & Unit weight
Dry density = wt. solid/Vttl.
Unit wt. of solid = wt. solid/Vsolid.
Submerged or buoyant unit wt. = Soil submerged weight/volume.
Bulk unit wt = total wt of soil/ total volume
Bulk γ = (G + es) γw / (1 + e) = G(1+ w) γw / (1 + wG)
Saturated γ = (G + e) γw / (1 + e)
Submerged γ = (G - 1)γw / (1 + e) = γ sat - γw = ½ γ sat ← Buoyant unit weight.
Dry γd = γ/1+w = G γw / (1 + e) = G γw / (1 + wG) = (1 -ηa) G γw / (1 + wG)
(γ/1+w)1 = ( γ/1+w)2 ← For numericals.
γ → Sat > bulk > dry > Submerged.
Important Relations
Se = wG
V solid = V/(1 + e) = Constant → V1 γd1 = V2 γd2.
Shrinkage ratio = γ dry/ γw.
Density index/Relative density/degree of density/relative compaction
Angle of internal friction of sandy soil.
Relative Compactness
Only for C-less soil or Coarse soil.
Id = (emax - e)/(emax - emin) = (1/γmin - 1/γ)/(1/γmin - 1/γmax)
0 ≤ Id ≤ 1
Densest Id = 100%, Loosest Id = 0%
Dense soil = 0.95 or Compact dense sand = 0.95.
better indication of denseness of solid than e & γd.
Relative compaction
Rc = 80 + 0.2 x Id
Id = density index
Specific Gravity
Specific gravity = mass solid/mass equal vol of water (at 4°C)
True G = γ solid/ γ w(at 4°C)
Mass specific Gm = G/1+e = γ total/ γ w = γd/γw
Determined at 27°C (indian std)
Organic soil = 1.2 - 1.4
Sand & inorganic soil = 2.6 - 2.75
Inorganic clay = 2.7 - 2.8
Soil containing Hematite = 5 - 5.3
G ∝ mineral content ∝ 1/amount of organic content.
G fine > G coarse grained soil.
In Lab true G at 10°C < 45°C
Note → Shrinkage ratio = γd/γw
i). Pycnometer
Only for coarse grain soil
Gs = (W2 - W1)/(W4 + W2 - W1 - W3)
For accurate G determination
ii). Density bottle method
Capacity of bottle = 50ml
Methods to find Water Content
Soil sample is heated for a period of 24 hrs at Temperature = 100 ± 10°C
i. Oven drying method
Simple, most accurate but time taking
Min quantity of soil for 2 mm IS sieve = 50 g
Temp = 105-110°C, Gypsum = 80° & Organic = 60°C
ii. Calcium Carbide
Quickest (5-7 min) → But not so accurate
CaC2 + 2H2O → C2H2↑(Acetylene gas) + Ca(OH)2
Use → Embankment of highway
iii. Radiation
in situ water content
iv. Pycnometer
G of only Coarse grain soil (C-less)
Hole dia in cap = 6mm
Volume of pycnometer = 900 ml
at 27°C,
G ≥ 2.6 Sand & inorganic soil.
w = [(W2-W1)/(W3-W4) x (G-1)/G] - 1
W1 = P, W2 = P +S, W3 =P+S+W, W4=P+W.
Gs = (W2 - W1)/(W4 + W2 - W1 - W3)
v. Sand bath method
Rapid field test hence not accurate
Highway construction,
No temp control & loss of structural water.
vi. Alcohol method
Quick field method
vii. Torsion balance method
Method for unit wt./density
i. Core Cutter method
Field method → Soft, fine grained clayey soil
Can't be used for Hard, Dry & Gravelly soils.
Steel dolly → ht = 25mm & dia = 100mm
ii. Sand replacement method
Field method → Gravelly, sandy & dry soil.
iii. Water displacement method
For cohesive soil only
Paraffin wax is used
vi. Nuclear Gauge density or Radiation method
Bulk density of in situ soil.
v. Rubber balloon method
In-situ density
Vol of pit is meas by covering the pit with plastic sheet & then filling it with water
wt of water calculated = vol of soil excavated.
INDEX PROPERTIES
index Properties helps in accessing engg behaviour (strength, shear, compressibility) & determining its classification accurately.
for Coarse soil → Grain shape & size ,relative density
for Fine soil → Atterberg's limit & consistency.
A) Grain Size
1. Sieve Analysis
Particle size > 75 μ
Smallest sieve size according to indian std = 0.045mm(45μ)
i. Coarse sieve Analysis
Used for gravels
4 sieves used → 80, 20, 10, 4.75mm
ii. Fine sieve Analysis
Used for sand
7 sieves used → 2mm, 1mm, 600μ, 425μ, 212μ, 150μ, 75μ
Sieve → designated by size of square opening in mm or microns.
Wet sieve analysis
Particle size < 75 μ (0.075 mm)
2. Sedimentation analysis
Based on Stokes law.
Particle size < 75 μ.
i. Hydrometer (< 75μ)
Grain size distribution & G of liquid (27°C)
Principal → Grain of diff size falls through a liquid at diff Velocity.
for fine grain soil like silt & clay
Based on Stokes law
Deflocculating/dispersion agent correction = -ve always
Meniscus correction = +ve always
Temp correction = +ve if T > 27 & -ve if T < 27
Corrected RH = RH + Cm - Cd ± Ct
ii. Pipette
Reading is taken directly.
Hydromet & pipette methods both follow the same principle but diff in taking samples/observations.
Hydromet is calibrated at 20°C
Stokes Law
d = 0.2mm - 0.0002mm
Settling velocity (Vt) = (Gs-1) γw d² / 18μ
Simplified version → Vt = 91.5d² (D → in mm, Vt → cm/sec)
Settling time = Ht of specimen/Vt
d > 0.2mm → Turbulent motⁿ
d < 0.0002mm → Brownian motⁿ
Grading of aggregate
Uniformly graded → Vertical line curve (Cu = 1)
Gap graded → Horizontal Curve line
Well graded → Curve line diagonally S-shape.
D60 > D30 > D10
Coefficient of Uniformity(Cu)
Cu = D60/D10
D10 = eff size of Particles.
Range of Cu ≥ 1
Cu is a measure of particle size range
Uniformly/poorly graded soil = 1
Poorly graded or uniformly graded < 4
Best filter material > 2
Slow sand filter = 1.5 - 3
Gravel > 4
Sand > 6
Well graded soil > 15
Coefficient of Curvature(Cc)
Cc = D30²/D60xD10
Shape of particle ditⁿ curve
Well graded soil → 1 ≤ Cc ≤ 3
√(Cu x Cc) = D30/D10
√(Cu/Cc) = D60/D10
Suitability Number
For rating of backfill
Sn = √(3/D50^2 + 1/D20^2 + 1/D10^2)
B. Atterberg's/Consistency limit
SL < PL < LL
For cohesive soil consistency indicates shear strength.
For normal consistency wc = 20 - 30%
Consistency of soil → Manifested by its resistance to Flow
Plasticity → Deformation but No vol. change.
Compressibility → Deformation with vol. Changes.
Soil mass will be in saturated state(S = 1) in liquid limit, plastic limit and shrinkage limit
Admixture of sand or silt to clay → Decreases both Liquid limit and plasticity index
Lime added to soil → ↓es PL, ↑es LL → ↑es Ip
Liquid Limit(LL)
LL ∝ consistency
indicates compressibility
by → Casagrande liquid device/tool and Cone penetration
at LL → τ = Negligible = 2.7KN/m² for all soil
Shear strength just developes
LL can be more than 100%
IS Sieve → 425 micron (0.425 mm)
Brass cup drop = 10mm on hard rubber base.
25 Blows & Groove cut = 12.7mm.
LL → Clay > Silt
Softer base → LL↑es
Fall cone test → cone depth penetration = 20 mm corresponding to LL
ASTM tool → to find LL when it is of more sandy soil
Flow curve
Flow index
If = Slope of Flow curve(wc vs logN) = (w1 -w2)/log(N2/N1)
flow index ∝ 1/shear strength
If → Rate at which soil mass loses its shear strength with an increase in water content
flow index represents τ variation with water
Plastic Limit
Soil rolled into 3mm thread starts to crumble
Organic matter mix → LL & PL ↑es
Clay → High LL & PL but LL >>> PL
Coarse grain soil (Sand, Gravel) → Low LL & PL but LL ≈ PL
Silt → No plasticity or Substantial plasticity
Shear strength in plastic limit state → Very little
Shrinkage Limit
Degree of saturation (S) = 1
if wc ↓es → no vol change, but weight loss
SL = (1/Gm - 1/G)x100
Gm = γd/γw
Mercurey → Used to determine dry volume of soil in SL test
Consistency index
Ic = (LL -W)/(LL - PL) = (LL - W)/Ip
Ic ↑es → Better foundation material
Liquid = 0
Very soft = 0 - 25 %
Soft = 25 - 50 %
Medium = 50 - 75 %
Stiff = 75 - 100 %
Very stiff = 100 %
Liquidity index/water plasticity ratio
IL = (W-PL)/(LL-PL) = (W - PL)/Ip
Ic + IL = 1 = Consistency index + Liquidity index
Shrinkage Ratio
Liquid used → Mercury
SR = Ratio of reduction in volume of soil mass expressed as % of its dry volume to the corresponding reduction in water content = mass G of its dry state
S.R. = γd/γw = (V1 - V2) / Vd(W1-W2)
Note → Specific gravity (G) = γs/γw
Plasticity index
Ip = PI = LL - PL
If LL - PL = (-ve) → Ip = 0.
Gravel & Sand = 0 ← Nonplastic
Silty-Sand < 7 ← low plastic
Silt = 7 - 17 ← medium plastic
Clay > 17 ← highly plastic.
Ip for Passing 425 micron sieve in case of subbase/base course < 6
Ip → Clay > Silt > Sand > Gravel
★ Ip (X1 + X2) = Ip1 X1 + Ip1 X2 (X2 = 100 - X1)
Plasticity → Property of soil which allows it to be deformed rapidly, without elastic rebound, without rupture and without volume change
Toughness index
It = lp/If = Plasticity index/Flow index
Gives idea about shear strength of soil at plastic limit
Range → 0 < If < 3
Friable (easily crushed) Soil < 1
Activity
A↑es → Vol.change ↑es
A = Ip / % clay (< 2μ)
Swelling potential is due to activity
Montmorillonite is responsible for Activity
Inactive < 0.75
Normal = 0.75 - 1.25
Active > 1.25
Thixotropy
Regain of shear strength with passage of time after it has been remoulded
Dilatancy or Reynolds dilatancy
Tendency of sand to expand by applying the shearing load
Sensitivity
St = qu undisturbed / qu disturb > 1 (at Same water content)
St↑es → thixotropy ↑es.
degree of disturbance of undisturbed clay sample due to remodelling is expressed by Sensitivity
Cu for undisturbed clay > remoulded clay
Determined by conducting Unconfined compression on both Undisturbed and Remoulded sample
IS 2720 (Part - V)
Determination of Plastic and liquid limit
Soil-water mix shall be left to stand for 24 hrs. → for clayey soil to ensure uniform distribution of moisture throughout the soil mass
CLASSIFICATION
Classification (IS-1498:1978)
1. The Unified Soil Classification System (USCS)
Given by casagrande
4 major group: coarse,fine,organic & peat(Pt)
general engg purpose
coarse grain → Based on size(sand,gravel)
fine grain → Based on plasticity chart.(fine sand, silt, clay)
Almost Similar to IS soil classification.
2. American Association of state Highway & Transportation Official (AASHTO)
into 8 groups (A1-A7 and A8 → for peat, muck)
For highways construction
Highway research → 7 types of soil (based on particle size & plasticity)
Group index
GI = 0.2a + 0.005ac + 0.01bd
Range = 0 - 20
if -ve it is reported as 0
GI ∝ 1/Quality of material
GI = 0 ← Good subgrade material
GI = 20 ← Very poor subgrade material
3. Indian standard soil classification system.
Modified USCS
Main improvement over USCS → division of fine-grained soil portion into six groups and inclusion of peat.
Divided into 3 major division → Coarse grained, fine grained and Highly organic soil
Coarse grain → Based on size, fineness, Cc & Cu.
Fine grain → Basis of PI, LL & Compressibility
★ BIS classified soil in 18 groups.
Clay → Aquiclude
Particle size ↓ → surface area ↑
Permeability↓ → compressibility↑
Sand particle are made up of Quartz (rock mineral)
Fine Grained Soil Classification
Soil classification chart → By Casagrande
By plasticity chart (Ip vs LL).
CL-ML soil → Ip or PI = 4 - 7
A-line → Ip = 0.73(LL- 20) – (i)
Ip = LL - PL – (ii)
eqⁿ(ii) > (i) → Clay (C) → Above A-line
eqⁿ(ii) < (i) → Silt(M) or Organic soil → Below A-line
U-line → Ip = 0.9(LL-8) → No soil lies above U-line
LL < 35% → low plastic (L) /low compressibility
35 < LL < 50 → intermediate plastic (I) /intermediate compressibility
LL > 50% → Highly plastic (H) /high compressibility
CH→ highly plastic clay, ML → Low compressibility inorganic soil
W → Well graded, P → Poorly graded
O → Organic soil
SP → Poorly graded sand
SM → Silty Sand, SC → Clayey sand
OH or OL → Clays organic soil
GW-GM and SP-SM → Coarse grained soils containing fines b/w 5-12%
Fineness modulus
CLAY MINERALS & STRUCTURE
Swelling of clayey soil directly depends on Type of clay minerals
Various clay minerals
i) Montmorillonite
Activity 1 - 7
Vanderwall force (weakest force)
Black cotton soil & Bentonite
Most common clay mineral
Most Active clay mineral
ii) illite
Activity 0.5 - 1
K(+ve) Bond (ionic bond)
Stiff clay & soft clay
iii) Kaolinite
Activity 0.4-0.1
Hydrogen bond (most stable bond)
China Clay G = 2.64
Gibbsite & Silica sheets through unbalance oxygen atoms
Porcelain
Made by heating material having Kaolinite
Steatic porcelain → 70 - 90 % silicate of magnesia
Important points
M > i > K > Silica ← Dry strength , PI , Plasticity, Permeability, swelling & shrinkage , Activity
K > i > M ← Grain size
Soil sheet → Silica, Gibsite(Al) & Brcite
Clay → ↑K, ↑Strength, ↓Compressibility
Soil Structure
Shape of clay particle → Flaky
i. Single Grained str
> 0.02mm
C-less soil , Gravel & Sand
ii. Honey combed str
0.02mm - 0.002mm
Gravity & surface electric force
C-less soil, sand & silt
Formed by disintegration of flocculent str under superimposed load
iii. Flocculated str
< 0.002mm
edge of face orientation & attractive force
clay particle settle on sea bad
low compressibility, High permeability & shear strength.
iv. Dispersed str (w of soil > omc)
Face to face configuration
More or less ∥ to each other.
Moisture content > optimum moisture content
Repulsive force
COMPACTION
Compaction
Measure in terms of dry density
Rearrangement of soil particles by dynamic pressure or Compression of soil by mechanical means or Reduction of air voids
↓es → Air void, Permeability, Settlement, undesirable volume change
↑es → γd, shear & bearing strength, stability
Methods of measuring field compaction → Sand replacement method, Rubber balloon method, Nuclear density gauge
No of blows for X volume = (X/1000) x 25
Compaction effort
MPT/SPT = 4.55 & SPT/MPT = 0.22
E = NnWh/V
Vol ∝ No of blows → V ∝ N
Relative Compaction = γdfield/γdmax lab
Input energy = Wt of hammer x Ht of drop
Increase in compaction effect → ↑es MDD, ↓es OMC
Compaction curve or moisture-density graph
γd vs wc
γd = (G γw) / (1+ wG/S) = (G γw) / (1+ e).
at OMC → S ≠ 1 but γd is max.
at zero air void line → S = 1
Order of MDD → Gravel > Sand > Silt > Clay
Well graded soil can be compacted more than poorly graded soil
Low plastic soil can achieve higher degree of compaction than Highly plastic soil
γd stops increasing after OMC → Water particles start occupying space of soil grains
↓es OMC → increasing compaction effect and coarse grains in soil
Unit wt of sand and clay increases → volume reduction Clay > Sand
Relative compaction
Rc = 𝛾dfield/𝛾dmax = Field dry density/Max dry density = FDD/MDD
Rc = (80 + 0.2 x Id) % (Id = density index)
Degree of compaction obtained in the field is measured by relative compaction
Compaction equipment
Cohesive soil → By application of Static pressure
Cohesion less soil → By vibration
Sheep foot roller → Kneading, Drum roller → Static compaction, Rubber Tyre roller → impact compaction, Vibratory roller → Vibratory compaction
Compacted soil
Better strength & stability - Fine grained soil → Dry of omc & Coarse grain soil → Wet of omc
CONSOLIDATION SETTLEMENT
Total settlement = immediate + Primary(1°) + Secondary (2°)
Consolidation is fⁿ of eff stress but not total stress
eo ↑es → Ultimate settlement decreases
Temp ↑es → Rate of consolidation ↑es
Compressibility → Field deposit > Laboratory Sample
Pressure metre test → Shear modulus of soil
immediately after loading → excess pore pressure = applied load
Loading → increase in total stress → Development of excess pore pressure → Decrease in excess pore pressure → increase in eff stress
In case of coarse grained sand having high permeability and low plasticity, 95% of consolidation occurs within 1 minute after application of load
Significant depth → depth up to which the stress increment due to applied load can produce significant settlement
Sand drains → Used to accelerate the consolidation
Long term settlement → Sand > Lean clay
i) initial Settlement/Consolidation
Expulsion of air, Sudden reduction in volume of soil mass under an applied load
Si = qB(1 - μ²)If/Es
Si ∝ If(influence factor/shape factor of foundation)
ii) Primary Settlement/Consolidation
Excess pore water due to ↑es total stress, Time dependent
∆H/Ho = ∆e/1+eo
∆H = mv ∆ s̅Ho = (CcHo/1+eo) x log(s̅2/s̅1)
∆H ∝ ∆σ
s̅2 = s̅1 + ∆σ
Happens more quickly in coarse-grained soil than in fine g soil
iii) Secondary Settlement / Consolidation or Creep
Plastic readjustment (Due to creep), Constant eff stress
Significant only for Highly plastic soil, Organic clay
Creep in soil predict by → Rheological models, Empirical method using creep data
Oedometer test / Consolidation test
1D consolidation (Zero lateral strain )
Object → to determine av, mv, Cv, Cc, K, pr-consolidation pressure
Drainage path → usually double drained
Max pore water pressure → at centre
Consolidation of sat clay → s̅↑es & pore water pressure↓es.
Oedometer was developed by Terzaghi
Note → Odometer measure Distance in vehicle
Compressibility Characteristics
OCR = Max pressure in past/ Present overburden pressure
OCR > 1 → Over consolidated soil
OCR = 1 → Normally consolidated soil
OCR < 1 → Under consolidated soil
Overconsolidated soil show less vol change
Highly Overconsolidated clay with high OCR → behaves like dense Sand
Pre-consolidated soil → Present eff overburden pressure is the maximum pressure that was subjected to in the past
Over-consolidated soil → Never been subjected to an effective stress greater than the existing pressure and soil is completely consolidated
Over consolidation → Due to erosion of over burden, melting of ice sheets after glaciations, permanent rise of water table
Under consolidation Clay → loss of shear strength is due to shock or disturbance
A-factor
fⁿ of OCR
Value of A = -0.2 to -0.3
Routine consolidation test (Lab)
Specimen thickness = 20mm
Dia = 60mm
General settlement formula
∆H/H = ∆e/(1+eo) = ∆V/V
e = wG (take S = 1 for test)
∆H = Hi - Hf = mv ∆ s̅Ho = (CcHo/1+eo) x log(s̅2/s̅1)
∆e = eo-ef
eo ↑ → ultimate settlement ↓
Note → when stress decreases void ratio → av ↑, mv↑, K↑
Compression index/Coeff of compression(Cc)
Helps to determine total settlement of clay layer
Cc = ∆e/log(s̅2/s̅1)
Cc ∝ ∆H ∝ LL
it is a constant value
Cc → Slope of virgin curve on semi-log scale or slope of linear portion of the pressure void ratio curve in the consolidation test
Cc = 0.009 (LL-10) ← Skempton's empirical index eqn for Undisturbed & medium sensitivity.
Cc = 0.007 (LL-10) ← Skempton's empirical index eqn for Remoulded & low to medium sensitivity.
Cc = 0.115Wn
Log(1) = 0, Log(2) = 0.30, log(3) = 0.477
Coeff of compressibility (Av)
Av = Strain/Stress = ∆e/∆ s̅
Unit → m²/kn
it is a Variable not constant
For 1D flow
∆σ = Small then Av = Constant
Coeff of vol change/compressibility (mv)
mv = Volume change or Vol strain per unit volume/increase in eff stress
mv = Av/(1 + eo) = ∆e/(∆ s̅ (1 + eo))
Unit → m²/kn
mv ∝ K
Terzaghi 1-D Consolidation Theory
δu/δt = Cv x δ²u/δz², where u = γwh
δu/δt = Rate of change of pore water with time
Analysis to behaviour of Spring piston model
Assumption → Only for 1-D flow (Vertical), Homogeneous, isotropic, incompressible & Laterally confined soil, Fully saturated, Laminar flow (Darcy law valid), e vs σ relation is linear and independent of time, for small load increment ratio, K and mv remains constant
Terzaghi considered only primary consolidation
Specimen (t) = 60mm
Spring-Cylinder analogy → To explain time-dependent deformation of saturated clayey soils
Isochrones
Solution of Terzaghi equation is represented by isochrone
Isochrones depict the variation of the pore water pressure along the depth of the soil sample
Isochrones vary with time
Initial isochrone for saturated clay layer consolidation with single drainage → Triangle
Coeff of Consolidation
Cv = K/mvγw = k(1+eo)/(Avγw) = Tvd² /t
Unit → cm²/s
Larger is Cv shorter it takes for full consolidation to occur
Cv is used for calculating time rate of settlement
Determination of Cv
a) Casagrande method (Logarithm of time fitting method)
Cv ∝ 1/LL ∝ 1/Plasticity
Cc ∝ LL ∝ Plasticity
b) Taylor's m (Square root time fitting )
Taylor curve is much more suitable as compared to casagrande method
Time factor(Tv)
Tv = Cvt/d²
One way drainage, Rock like → d = H
Two way drainage, Soil like → d = H/2
U ≤ 60% → Tv = πU²/4
U > 60% → Tv = 1.781 - 0.933log(100-U)
To = 0, T50 = 0.196, T60 = 0.287, T90 = 0.848.
Consolidation time(t)
t = Tvd² /Cv = Tvd²mvγw/K
t one way drainage = 4 x t two way drainage
t ∝ Compressibility
t ∝ 1/Permeability
t ∝ Size of soil mass
independent of the Stress change (∆σ)
Degree of consolidation(U)
U = Settlement any time/Final settlement
U = ∆h/∆H = (eo - e )/(eo - ef)
For numerical use → πU²/4 = Cvt/d²
U ∝ Tv ∝ Cv ∝ t ∝ 1/d²
Expansion ratio of soil = ∆h/Hi
PERMEABILITY (Hydraulic Conductivity)
Permeability → Property of soil mass which permits the seepage of water through its interconnecting voids or due to which water percolates through soil mass
Transmissibility → Capability of soil or rock to transmit water through itself while considering unit width and full depth is under unit hydraulic gradient
infiltration → Absorption of water by surface of soil
Specific surface = D/6 (D = Particle size)
Darcy Law
1D flow, homogeneous, isotropic, fully saturated soil, Laminar flow, Re ≤ 1, fine grounded soil, for sand, silt, clay and not for gravel, should follow continuity conditⁿ, soil is incompressible under stress
V ∝ i → Seepage velocity ∝ Hydraulic gradient
Q = KiA = KhA/L
Darcy law is based on Naiver stokes eqⁿ of motion
Continuity eqn
V = Ki = Q/A
Q = KiA
i = ∆h/L
V → Superficial/avg velocity/Discharge velocity.
K → Coeff of Permeability(m/day, cm/sec)
Seepage or Actual velocity
Vs = Kpi = V/η = Ki/η
Vs > V
Coeff of percolation
Kp = K/η (m/s)
η ← Porosity
Coeff of Transmissibility
T = KH
H ← Thickness of aquifer
Coeff of absolute / intrinsic/Specific permeability
Ko = K.μ / γw = K.v/g
Unit → cm² or m²
Factor affecting K
K ∝ D10²
K ∝ e³/ 1+e ∝ e² → k ∝ void ratio
K ∝ γw/μ
K ∝ 1/γsoil
K ∝ 1/impurities
K ∝ 1/organic matter
K ∝ 1/adsorbed water
K ∝ Degree of saturation
K ∝ Temp ∝ 1/μ
K ∝ 1/(specific surface area)^2
K ∝ size (Particle size ∝ 1/compressibility)
K ∝ 1/compressibility
s̅↑ → e↓ → K↓
K ∝ γ fluid, Temp ∝ 1/μ
K ∝ 1/γsolid ∝ 1/compressibility
K ∝ 1/entrapped air
K ∝ 1/eff stress on soil
Permeability is minimum at omc and max dry density
Permeability also depends on → shape of particle, str of soil mass, properties of pore fluid
Determination of K
A) Laboratory methods
i. Constant head method
Coarse grained soil & Pervious soil like sand & gravel
K = VL/thA = Q/iA
i = h/L
Q = kia = V/t
ii. Falling/Variable head method
Cohesive soil, fine soil & impervious soil like clay
K = (2.303aL/At) x log10(h1/h2)
h2 = √(h1.h3) → if t h1 to h2 = t h2 to h3
B) Field test
Draw down or depression head → Depth of water level below ground level after pumping
i. Pumping out
Best for → K of soil deposit in-situ
Large Area & Homogeneous coarse grain soil
Radii of influence → R = 3000d √K → Sichardt formula → d = drawdown
Unconfined aquifer → K = 2.303QLog(R/r) / π(H1²-H2²)
Confined Aquifer → K = 2.303QLog(R/r) / 2πD(H1²-H2²)
Coeff of transmissibility → T = Q / 2.72(∆S) → Confined aquifer
Dupit's Theory → Unconfined Aquifer
Thiem's eqⁿ → Confined Aquifer
ii. Pumping in
Small Area or Project, Economical but less reliable
C) Indirect method
i) From consolidation data
ii) From particle size & Specific surface area
i. Horizontal Capillarity test /Capillarity permeability test
For partially saturated soil
ii. Kozeny - Carman equation
K = (1/c) x (γw/μ) x (e³/1+e) x D10²
K ∝ D10²
K ∝ e³/ 1+e ∝ e²
K ∝ γw/μ
iii. Allen Hazen's formula
K = C D10² (cm/s)
C = 100, D10 → cm
iv. Louden's formula
log(KS^2) = a = bn
v. Tarzaghi's eqⁿ
K= 200e²D10²
vi. Consolidation eqⁿ
K = CvMvγw
Permeability coeff values
Gravel > 1 cm/s → Very pervious
Sand = 1 to 10⁻³ → Pervious
Silt = 10⁻³ to 10⁻⁶ → Poorly/Semi pervious
Clay < 10⁻⁶ cm/s → Impervious
K → Gravel > Sand > Silt > Clay
Imp points
Kh = ΣKiHi / ΣHi
Kv = ΣHi / Σ(Hi/Ki)
Kh > Kv
Transmissivity = ΣKiHi
K1/K2 = tanϕ1 / tanϕ2
Eff permeability k' = √(Kx.Kz)
EFFECTIVE STRESS
Eff stress concept developed by Terzaghi & Applied for Fully saturated soils
it is Not a physical parameter & can't be measured
Eff stress on soil is due to weight of water present in pores
Eff stress is function of → Particle contact force
Eff Stress = Total stress - Pore pressure → s̅ = σ - U.
eff stress in Hydrodynamic flow → s̅ = σ - U ± izγw (+ Downward flow, - Upward flow)
Eff stress on soil → Decreases both void ratio and permeability
if fluctuation in the level of free water above ground surface → would not result in any change in eff stress at any depth
Rise in water table → Decreases eff stress
Fall in water table → increases eff stress.
Capillary rise or rise in capillary zone → increases eff stress
if external overburden F/A = 0 then total stress is called Geostatic stress
Eff vertical stress due to self wt of soil = γz
Eff Pressure → Pressure transmitted through grain to grain at the contact points through a soil mass
Pore water pressure or Neutral pressure (U)
U = γwZ
Measured by → Piezometer or a stand pipe
∆ σ increments cause an increase ∆U = ∆σ at t = 0.
Tensiometer → Pore water pressure
Capillary zone → Pore water pressure = (-ve)
Dense sand and overconsolidated soil → -ve pore pressure
Capillarity
Due to Surface Tension
h = 4σcosθ/ρgd = 0.3/d (h = cm, d = cm)
Capillary rise in soil → (hc) = C / e D10, (C = 0.1 - 0.5 cm²)
h ∝ 1/d
h = (σ/𝛾w) x (1/R1 + 1/R2) → R1,R2 are radii of curvature of a non-uniform meniscus in two orthogonal planes
h → colloids > clay > silt > sand
in Capillary Zone or Fringe → Pore water pressure = (-ve) & Tensile
Capillary Zone → Total stress = Pore water pressure (proven by terzaghi)
Capillary pressure & Capillary rise → Coarse < Fine grain
Capillary water → increases bearing capacity
Bulking of sand occur due to capillary rise
Capillary rise is controlled by pore size and not the grain size
SEEPAGE
Drainage of fine grained cohesive soil → Electro osmosis methods
Aquitard → Poor permeability but seepage is possible
Direction of seepage/flow →Perpendicular to equipotential lines
Sheet pile → to Prevent seepage of water
Laplace eqⁿ in 2D flow
δ²ϕ/δx² + δ²ϕ/δx² = 0
isotropic medium → δ²H/δx² + δ²H/δx² =0
Non isotropic → Kxδ²H/δx² + Kyδ²H/δx² =0
Assumption → Homogeneous , S = 1, Laminar flow, Darcy law valid
K = ³√(Kx.Ky.Kz)
Flow chart/Flow net
Based on Darcy Law
Graphical representation of 2D steady groundwater flow
Graphical solution of Laplace equation is flow chart
Equipotential line (Equal head) vs Flow heads
Can't be drawn when flow is governed by gravity.
Configuration of flow nets depends upon the boundary condition of flow
Methods → Electrical analogy method, Hydraulic model, Analytical method, Graphical method, Capillary flow analogy, Sand model.
Flow net for transformed section → Shortening horizontal dimension by √(kz/kx)
Application of flow Net
Seepage Q, Seepage P, Uplift P, Hydrostatic pressure, Exit i, Pore water pressure
i) Seepage discharge
Q = KH Nf/Nd
Shafe factor = Nf/Nd ← Depends on boundary condtⁿ
Flow channel (Nf) = Flow line(Nw) - 1
Equipotential drop(Nd) = Equipotential line(Nϕ) - 1
Q also depends on Length of flow path
ii) Seepage pressure
SP = ywh = izyw = ∆hzyw/L
SP ∝ i exit
Pressure exerted by water on soil
Always act in direction of flow
Parallel to streamline & Perpendicular to equipotential line
iii) Uplift pressure
Pu = ywH
Reduces self weight of dam
Shape → Trapezoidal
Depends on → Head at u/s, head at d/s
iv) Exit gradient
Gradient of the piezometric head at exit point of a streamline
ie = Total head loss/(Number of potential drop x Length of flow path for a square)
ie = Δh/L = head loss/length of seepage
Seepage line
Line developed in c/s of earthen dam, below which the soil is saturated and pressure everywhere on that line is atmospheric
Phreatic Line
Uppermost line of seepage in Earth dam or upstream slope of an earthen dam under steady seepage condition
A streamline, a flow line
Follow path of base parabola
On Phreatic line & Above → Hydrostatic pressure = Atmospheric pressure
Below PL → Hydrostatic pressure = (+ve)
PL is kept within the body of the dam → By providing horizontal drainage filter at the D/S face
Piping
Cohesionless soil
i ≥ ic → Piping failure
Uplift force or upward seepage pressure ≥ Submerged unit wt of soil
Prevented by → increasing the seepage length, filters and sheet piles at downstream, increasing pressure due to body forces
To prevent piping failure → (D15/D85) filter < 5 or size of filter material = 5 x size of foundation soil
Seepage flow through a porous foundation or body of a dam piping is due to dislodging of soil grains by percolating water
Quick sand condition/Boiling of sand
Hydraulic condition → eff stress reduced to zero and sand starts floating over the water or head causing upward flow = stress from top or lose shear strength and behave as a fluid
s̅ = γ'z - Ps = 0
Sand & Coarse silt
Critical hydraulic gradient(icr)
Hydraulic gradient corresponding to zero resultant body force
icr may occur → flow takes place through the soil in the direction opposite to gravity
icr = (G -1)/(1 + e) = γ sub/ γ w = (G - 1) (1 - η)
Factor of safety = icr/ie
Max permissible upward gradient = icr/FOS = h/L = (G -1)/FOS(1 + e)
icr > i exit → Safe
in situation of boiling → icr = 1.0 (if G = 2.65 & e = 0.65)
Acc to khosla theory → icr for alluvial soil = 1.0
SHEAR STRENGTH
Consistency indicates shear strength
Shear strength parameters (C , ϕ ) are not inherent properties ,they are related to type of test & condition under measured
Shear strength is due to cohesion, internal friction and structural resistance.
Shear failure → angle of obliquity is max
Penetration test → Field test ( τ )
Failure on soil occurs by shearing never by crushing
τ ∝ eff stress (Not total stress)
Cohesionless soil (C = 0) → τ ∝ σ ∝ rate of loading
Sandy soil → Most likely to be the failure plane is plane with maximum angle of obliquity
Dilatancy → Expansion of soil under shear
Most of shear test are done on equipment which are Strain-controlled
Shear failure indicates lateral displacement of soil
Shear strength of clay tests can not be done without undisturbed sampling
Electro osmosis → Stability or shear strength of fine soil (clay) can be increased by draining them with the passage of direct current through them
Max shear stress in a uniaxial loading occurs at a plane → 45° and 135°
Pure clay → Failure plane carries max shear stress
Other Soil → Fails at a shear stress less than maximum
Sand pile → used to increase shear strength
Mohr’s strength theory
Material fails essentially by shear
Ultimate strength of material is determined by the stress in the plane of slip
Failure criterion is independent of the intermediate principal stress
Coulomb equation
τ = C + σ tanϕ
Terzaghi modification
τ = C' + ⁻σ tanϕ'
⁻σ = σ - u
u = pore water pressure
Angle of failure (Ø)
Ø = 45 + ϕ/2 → with major principal plane
ϕ = angle of shearing resistance or internal friction
Angle of internal friction(ϕ)
Pure clay → ϕ = 0°
Clay → ϕ = 5°-20° (due to quantity of sand) ← as per UU test
Round grained loose sand → ϕ = 25°-30°
Angle of obliquity(α)
Angle made by normal stress with tangential stress
tan(α) = τ/σ
At max α → α = ϕ → shear failure of soil takes place
i) Direct shear test or Shear box test
C-less soil → Sand & gravel not for clay
eff σ = total σ → bcz U = 0
τ = C' + s̅tanϕ'
Quick, inexpensive & simple
Dial gauge → Shear & vertical deflection are measured
More stress at the Edges & less in the centre
Proving ring → To measure Shear load
For estimating bearing capacity of a saturated clay deposit the shear strength parameter should be determined from direct shear test
Disadvantages
Drainage condition uncontrolled
Pore water pressure can't measured → eff stress can’t determine → not suited for determining shear parameters of a clay soil
Failure plane predetermined & always horizontal
Non-uniform stress distⁿ
Volume change can’t be measured.
ii) Vane Shear Test
Suitable for soft saturated clay & silt, Plastic cohesive soil which is very sensitive
Field test → Soft clay, Sensitive soil, Cohesive soil, Plastic clay soil
Lab test → Liquid limit of silty clay and Shear parameters of
Also used to find sensitivity
Sensitivity = Cu undisturbed / Cu remoulded
Shear strength = Undrained cohesion → τf = Cu = qu/2
τ f = C = T /πd²(h/2 + d/6) ← 2 way shear top & bottom & if nothing is given
τ f = C = T /πd²(h/2 +d/12) ← One end shear from bottom
Laboratory vane → Height/diameter = 1.67 ≈ 2
iii) Triaxial Test
All type of soil
To determine shear strength of soil under Lateral confinement
To assess shear strength parameter of the soil
Specimen → Length/Dia = 2 - 2.5
Pore water pressure & vol. Change can be measured
Drainage condtⁿ best controlled
Axial strain & deviator stress are determined
Stage 01 → Cell pressure or consolidatⁿ test
Stage 02 → Shear stage or deviater stage
σ 1 = σ 3 + σ d
Cell pressure = σ 3 = σ c
σ1 = σ3 tan²(45 + ϕ/2) + 2C tan(45 + ϕ/2)
Saturated Clay → τ = Cu = (σ1 - σ3)/2 = σ d/2
Undrained triaxial compression test → ϕ = 0 → σ1 = σ3 + 2C = σ3 + 2τ
Sin ϕ = (σ 1 - σ 3)/(σ 1 + σ 3)
μ = σ 3 / (σ 1 + σ 3)
inclination with horizontal (α) = 45 + ϕ/2 → ϕ = 2(α - 45)
Confined compressive strength = σ d at failure = P/Af
A at failure = (V - ΔV)/(H - ΔH)
Type of TT
UU → Clay, quick test(15min), Drainage not permitted at any stage
CD → Sand, slow test, Long terms stability (excavated clay), Pore water pressure = 0
CU → Clay dam embankment
UD → Physically impossible
For saturated sand can exhibit an angle of shearing = 0 → it can be obtained in case of UU testing
Representation of TT
Pure clay ϕ = 0 ← Undrain test on sat clay
CD test on NC clay then clay behave like sand (C = 0)
For C-ϕ soil → CD test on OC clay behave like silt
Demerits of triaxial test
Takes longer period under drainage conditions than a direct shear test
Uneconomical
Soil is assumed isotropic while in actual Anisotropic in nature
At large strain measure of c/s area is not accurate
D) Unconfined Compressⁿ Test
Undrained test → No moisture loss
Cohesive soil (Saturated clay & silt) not for coarse grain soil
Special case of TT → σ 3 = σ c = 0
σ1 = qu = 2Ctan (45 + ϕ/2)
For saturated clay ϕ = 0 → qu = 2C → Unconfined compressive strength = 2 x Shear strength = 2 x Cohesion
θ = 45 + ϕ/2, ϕ = angle of shearing resistance, θ = angle made by Failure plane to the horizontal
Skempton Pore Pressure Coeff
Parameter B
B = ∆Uc/∆σc
Range → 0 ≤ B ≤ 1
Dry = 0
Fully saturated soil = 1
Parameter A
OC soil = - 0.5
Loose soil = 3
Dilatancy: expansion of soil under shear
Corrected A = Ao / (1 - εv) = V / (h - ∆h)
Dry loose sand → Angle of shearing
Resistance → Angle of internal frictⁿ
Shear test on cohesionless soil
Initial e < critical e → Dense soil → Volume decreases initially then increases
Initial e > critical e → Loose soil → Volume Decrease
Liquefaction of soil
Liquefaction → In sands during earthquakes instantaneous pore pressure are likely to develop leading to sudden and total loss of shearing strength or soil loses its shear strength due to oscillatory motion
With Sandy soil not in normal clay but highly sensitive clay may undergo liquefaction under vibrations
May occur if → Liquid limit < 35 %, wt of particles (< 0.005 mm) < 15% of dry wt of soil
Most susceptible to liquefaction → Saturated fine and medium sands of uniform particle size
Behaviour of sand mass to cause liquefaction during an earthquake largely depends on → Relative density of sand
Sand column → Reduce damage due to liquefaction on of saturated granular soils during EQ
Note → Quick condition and liquefaction of saturated sands are based on similar phenomenon
EARTH PRESSURE & RETAINING WALL
Cohesive soil are poor for backfill bcz of large lateral pressure
Depth > 3.0 m → Shallow pits should be provided with lateral support
Anchor theory of earth pressure is directly applied to bulk heads
Pressure = σ h = K x σ v = KγZ
Force = Thrust = Pressure per unit length = Total pressure = ½ K γ H²
Type of Lateral Pressure
i. Active earth pressure (pa)
Wall move away backfill
Failure plane = 45 + ϕ/2
Ka = (1-sin ϕ)/(1+sin ϕ) = tan²(45 - ϕ/2)
Active earth pressure decreases due to increase in wall friction
Ka means effective stresses
ii. Passive (pb)
Wall move towards backfill
Failure plane = 45 - ϕ/2
Kp = (1+sin ϕ)/(1-sin ϕ) = tan²(45 + ϕ/2)
iii. Earth pressure at Rest
Wall doesn't move
Theory of elasticity
ex. Earth pressure behind bridge abutment
Ko = μ/1-μ
C-less soil (C = 0) → Ko = 1 - sinϕ (Jacky formula)
Heavily over consolidated soil → Ko > 1
Coefficient of lateral earth pressure(K)
K = (σ h effective)/(σ v effective)
Ka x Kp = 1
Kp ≥ Ko ≥ Ka → Pp > Po > Pa
For ϕ = 30° → Kp = 3, Ka = 1/3, Ko = 1/2
For ϕ = 0° → Kp = Ka = Ko = 1
ϕ ∝ Kp ∝ 1/Ka
Earth Pressure Theory
Classical EP theory → Rankine theory, Coulomb theories
1) Rankine Theory
For Cantilever & Counterfort wall
Soil semi-infinite, homogeneous, isotropic, Dry & cohesionless, Backfill is horizontal, Back of wall is vertical & smooth, Fraction = 0 → b/w wall & backfill, Yielding about base
Pp = Kp γZ + 2C√kp
Pa = Ka γZ - 2C√ka
Due to cohesion → Pa ↓es & Pp ↑es
i. Active earth Pressure on cohesive soil
Pa = KaγZ - 2C√Ka
If q surcharge per unit area → Pa = Ka(γZ + q) - 2C√Ka, F = ½ K γ H² + KqH
Tension crack
Zo = 2C/γ√Ka
Critical or Theoretical or Max depth
Ho = 4C/γ√Ka = 2Zo
Ho = An unsupported vertical cut that may be made in cohesive soil or a height of Maximum depth of unsupported cut
Cohesive strength or Cohesion (C) = Hoγ/4 (Take Ka = 1 as for clay ϕ = 0°)
ii. Cohesionless soil on a vertical smooth wall
Pressure → Pa = Ka γ Z, Pp = Kp γ Z
Thrust (Total pressure) → Fa = ½ Ka γ H² , Fp = ½ Kp γ H²
Passive state → Minor stress is vertical, major stress is horizontal
Active state → Minor stress is horizontal, major stress is vertical
iii. Soil with inclined backfill
Pa = Ka σ = Ka γ z cos β
Fa = ½ Ka γ H²cos β
σ = γ z cos β
2) Coulomb's wedge Theory
Used for Gravity & semi gravity wall
Wall surface is rough, Backfill is Cohesion-less , dry, homogeneous, isotropic & ideally plastic material
Sliding wedge itself act as a rigid body
Active earth pressure slides the wedge down and outwards on a slip surface
3) Rebann's method
Graphical method for determination of earth pressure
Retaining Wall
Structure retain ground surface
FOS sliding = Resisting force /Sliding force ≥ 1.55 → Sliding force/Resisting force ≤ 0.645
Lateral earth pressure ∝ internal friction of soil
Flexible retaining wall → Mechanically stabilised
Rankine theory → Cantilever retaining wall, Counterfort retaining wall
Coulomb's theory → Gravity retaining wall , Semi gravity retaining wall
Concrete retaining wall rankine theory is not valid bcz friction exist
a) Gravity RW
Resistance by self wt
ht ≤ 3m
b) Cantilever RW
ht = 6 - 7m
if ht > 6m → counterfort retaining wall
FOS ≥ 1.55 Against sliding
c) Buttress RW
More efficient & more economical than counter fort
Buttress provide Lateral support to wall
SHALLOW FOUNDATION
To ensure uniform pressure distribution, the thickness of the foundation is decreased gradually towards the edge.
The weight of foundation = 10 % of wall weight (Assumption)
Depth of foundation D = 0.00755 α √P
Self weight of footing is also considered for calculating the upward pressure on footing
The proportioning of footing is more often governed by its Service load.
The width of footing for two equal columns is restricted by the shape of footing adopted is Rectangular
Soling → A layer of brick/stone below the foundation concrete for better strength of foundation
Underpinning → Arrangement of supporting an existing structure by providing supports underneath
Weaker soil → Grillage footing, Column footing, Raft footing
Pier footing → For heavy structure on sandy soil
Performance → Raft foundation > Combined footing > isolated footing
Floating foundation → The net soil pressure beneath the foundation structure is zero, weight of excavated soil = Superimposed load, to restrict settlement of soft clay/silts
Min depth of foundation of footing in clay soil = 900mm = 0.9m
Significant depth → The depth up to which the stress increment due to superimposed load can produce significant settlement
i. Strip/Continuous foundation
Number of columns constructed in a row
L >>> B or L/B ≥ 10
Load intensity is given in terms of Load per unit length
ii. Raft/Mat foundation
Area excess 50% of plan area
Use → Soil has low bearing capacity, Heavy building loads, Super structure is sensitive to Differential settlement, Structure on black cotton soil
Used to reduce settlement above highly compressible soils by making wt. of str + raft ≈ wt of soil excavated
iii. isolated footing
iv. Strap footing
To transfer the moment b/w two adjacent footings
v. Spread footing
Cantilever footing
Combined footing
When column are very close to property line
General requirement of footing
Settlement within permissible limits
Safe against Shear failure
Located in such depth that seasonal volume change doesn't affect its performance.
Terzaghi → Df/B ≤ 1(shallow footing) & Df/B > 1 (deep )
Skemptons → Df/B ≥ 2.5( Deep foundation)
Bearing capacity
FOS = qnu/qns = (qu - γD )/qns = (qf - γD )/q
FOS = Load/qu
FOS → To ensure the soil behaviour to be elastic at working load
No FOS used for settlement analysis
qu = max gross pressure before soil fails in Shear
Criteria for BC → Shear failure and settlement
Net ultimate bearing C → qnu = qu - γDf
Net safe bearing C → qns = qnu/FOS
Gross safe bearing capacity → qs = qns + γ Df
Max load carrying capacity = qns x base Area
qu > qnu > qs > qns
Area of footing = 1.1 x Load/Safe bearing capacity
qu of circular/qu of square = 3/4 = 0.75 → if dia = width
qnu of circular = qnu of square → if dia = width
qnu of strip footing on clay > Square footing of same size
To avoid tension → B x L = (P/q) x (1 - 6e/L)
minimum bearing capacity → Groundwater table at the location of the ground level
Gross safe bearing capacity → No shear failure
Safe Bearing pressure/unit soil Pressure/net safe settlement Pressure → No risk of shear failure on max gross pressure, net pressure the soil can carry without exceeding settlement
Ultimate bearing capacity → Soil fails in Shear or load at which soil fails
Allowable Bearing capacity → No settlement & shear failure at max net intensity of loading
Safe bearing capacity of a cohesion less fine loose dry sand = 100kN/m^2
A} Analytical method
Max deformation or large settlement → Punching shear failure
i) General shear failure
Soil with relative density > 70%
Brittle type shear-stress curve
Failure due to tilting of foundation
All the three zones of failure develops fully
ii) Local shear failure
Loose sand & soft Clay, Soil with relative density = 30 - 70%
SPT N ≤ 5 & relative density (ID) < 30%, Vertical strain > 90%
Foundation doesn't tilt
Failure is not sudden and preceded by large settlement, highly compressible soils, Loose sand soft Clay in shallow foundation
iii) Punching shear failure
Very plastic soil, Soil with relative density < 30%
Deep foundations generally fail by punching only
No tilting of foundation
Ultimate load cant be clearly recognized
B} Building codes
i) Rankine's method
For ϕ soil → Generally to find Df
qu = γ Df (Kp)² = γ Df tan⁴( 45 + ϕ/2 )
Df = (qu/γ) x (Ka)² = (qu/γ) x tan⁴(45 - ϕ)
ii) Prandtl method
C-ϕ soil
Strip footing placed on the ground surface sinks vertically downwards into the soil at failure
iii) Terzaghi method
C-ϕ soil
Underestimate bearing capacity of soil
Assumption → Strip/continuous footing (L >>> B), Shallow foundation (D/B ≤ 1), foundation base is rough, general shear failure
General shear failure governed by Mohr's criteria
Soil wedge immediately below footing → Remains in state of Elastic equilibrium
Nc, Ny, Nq → Function of angle of shearing resistance (ϕ) only
ϕ ↑es → Bearing capacity increases
Strip/Continuous footing → qu = CNc + γDNq(γ up to depth of footing) + 0.5 BγNy( γ bellow depth of footing)
Square footing → qu = 1.3CNc + γDNq + 0.4 BγNy
Circular footing → qu = 1.3CNc + γDNq + 0.3 BγNy
Rectangular footing → qu = (1 + 0.3B/L)CNc + γDNq + (1 - 0.2B/L)BγNy
Local shear failure Cm → ⅔ C & tan ϕm = ⅔ tan ϕ
Cohesive Soil or Clay (ϕ = 0) → Nc = 5.7 = π +2, Nq = 1, Ny = 0 and qu → independent of size of footing i.e, Width and depth
qnu = qu - γD
Eff of water table
The rise of water table in cohesionless soil up to ground surface ↓es the Net ultimate bearing capacity by 50%.
Water table at B/2 → ↓es by ¾th of strength
Water table below a depth = Df + B → Rr = Rq = 1
Water table at ground level → Rr = Rq = 1/2
iv) Skempton's method
For pure cohesive soil
qnu = CNc
Nc = 6(1 + 0.2Df/B)
Coeff B = ∆Uc/∆σc → Dry soil = 0, Sat soil = 1
Coeff A → OC soil with OCR = -0.5
C can be found → By i) U-U test, ii) Vane shear test, iii) Unconfined compression test.
C} FIELD TEST
i. Standard penetration test
Relative density, Bearing capacity & Settlement of granular soil
For Granular soil or cohesionless soils
Gives idea about Unconfined compressive strength of clay
More suitable to find qu
Impact = 65kg, Free fall = 75 cm, Penetration = 30cm
Water level in the borehole is always maintained → Slightly Above the groundwater level
Blow require = N (Penetration no.)
N is calculated for depth from D + (1.5 to 2) B
N > 50% of Avg N → Rejected & Find a new value
Blows recorded 10/20/30 → N = 20 + 30 = 50
If energy efficiency is 60% → N = N/0.6
Overburden correction
N1 = No [350/(σeff + 70)] For (σ ≤ 280 Kn/m²)
Overburden pressure increases → Standard penetration value increases
Dilatancy correction:
N2 = 15 + ½ (N1 - 15) For N1 > 15 for fine silty saturated sand
Cohesive Soil (Clay)
Cohesionless Soil (Sand)
ii. Plate load test
Settlement of plate not soil
Cohesionless or granular soil only
Short duration test
Min settlement = 25mm
Plate t ≥ 25mm
Plate size = 300, 450, 600, 750mm → Square in section
Gravely and dense sand → plate size = 300mm
Width of test pit = 5 x Plate width
initial pressure = 7 kpa = 70gm/cm²
Settlement → Shallow foundation/Test plate ≤ 4
Used to calculate
a) Allowable bearing capacity based on settlement criteria
b) Ultimate bearing capacity based on shear criteria
Granular Soil
quf / qup = Bf / Bp
qu ∝ B
Sf/Sp = [(Bf/Bp) x (Bp + 0.3) / (Bf + 0.3)]²
All → in meters
Clayey Soil
quf = qup
Sf/Sp = Bf/Bp
iii) Static cone penetration test
Soft clay, Silt, Fine to medium Sand and silts deposit
Cone area = 10 cm²
Apex angle = 60°
Pressure & settlement distribution
Settlement (S) rigid = 0.8 x Settlement flexible
Total vertical settlement of a rigid foundation = 1.4 x total vertical settlement at the centre
i. Flexible footing
Contact pressure uniform
Settlement distribution
Clayey soil → Max at centre & min at edge
Granular soil → Max at edge & min at centre
ii. Rigid footing
Settlement uniform
Pressure distribution
Clayey → max at edge & min at centre
Granular → max at centre & zero at edge
Max differential settlement
Granular Soil(Sand) = 25mm → for both isolated and raft
Clayey soil = 40mm → for both isolated and raft
Diff settlement = Angular distortion x Spacing b/w columns
Total Permissible settlement or maximum settlement
isolated footing → Clay = 65m, Sand = 40mm
Raft → Clay = 65 - 100, Sand = 40 - 65mm
Multistory building having isolated foundation on sand = 60mm
Rigidity Factor
Ratio of the total settlement of rigid foundation to the total settlement at the centre of flexible footing
Rigidity factor 0.8 for computing settlement of rigid footing
DEEP FOUNDATION
Proportioning of footing → Governed by service load
Service load = Dead Load + 0.5 x Live load ← Ordinary building
Cantilever sheet pile type cofferdam is not preferred to large leakage and flood damage problems
Types → Pile foundation, Well/Caisson
While driving a large number of piles in loose sand it is advantage to follow a sequence of pile driving such that the piles … periphery are driven first and inner piles are driven later
Depth of exploration = 1.5 x Width of footing
Thickness of concrete tops of piles > 300 mm
Piles
Slender member transfer its load to surrounding soil or bottom end
Piles are provided → When Area rqrd > A available
Pile as a Column → One end fix & one end free
Fully fixity at the column may be valid for column supported by → thick pile cap, a raft foundation, an individual footing on rock
Sand pile → when weak foundation soil is to be compacted
Sheet piles → Both load bearing and non-load bearing
Fender piles → used to protect concrete deck or other waterfront structure from the abrasion or impacts of ships and vessels
Fully fixity at the column may be valid for column supported by → thick pile cap, a raft foundation, an individual footing on rock
Method to determine the ultimate load capacity of a pile → Single tangent, Double tangent, Vander veen’s method
Types of Piles
Based on mode of transfer of load
Point/End bearing pile → Transfer heavy loads to strong stratum, Obtains most of its load carrying capacity at the base of pile, Neutral planes will be located close to the base of compressible stratum
Friction or Floating pile → Soft or Stiff clay
Combined end bearing and friction pile →
Based on function/Action
Load bearing pile → Transfer load of structure
Tension or Uplift P → Hydrostatic pressure or Overturning moment, Uplift load
Compaction pile → Compact loose granular soil, Takes No load
Batter pile or Raked → Resists Heavy lateral load (inclined or horizontal loads)
Sheet pile → Retain soil filling
Dolphins & Fender pile → Protect waterfront str from impact from ship & floating obj
Anchor piles → Anchorage against horizontal pull, resist uplift force
Based on material and composition
Timber, Steel, Concrete, Composite piles
Based on method of installation
Driven piles, Bored and cast in-situ, Driven and cast in-situ, jack, Screw piles
Raymond pile → Cast in-situ concrete pile, Underwater structure, Additional pile driven to increase capacity
Load carrying capacity → Bored pile = 2/3 - 1/2 of Driven pile
Cased cast in-situ concrete piles → Swage piles, Frankie pile
Min centre to centre spacing (IS : 2911)
Friction piles = 3D
End or point Bearing piles = (2.5 - 3.5)D
Loose type sand = 2D
Piles under marine structures and wave action → 3D
Precast piles
Precast pile → Circular is best
Precast piles are generally Square with corners chamfered
Pile suspended at one end → Max BM = WL²/8
Pile suspended at two points → Max BM = WL²/47
Pile suspended at three points → Max BM = WL²/90
Erection Pile → one end on ground & lifted from x = 0.293L from other end & Max hogging & sagging BM = ± WL²/23
Negative skin friction
Exert a downward drag force
Fill material or Soil is soft or very Loose
it Reduces load carrying capacity of piles
Developed → When pile is driven through a recently deposited clay layer, due to a sudden drawdown of water table, when fill material is Cohesionless soil or deposited over layer of soft soil (Peat), Load < Design load, Settlement of pile < Surrounding soil
FOS = Qup/(Working load + Qnf) → Qnf = Negative skin friction resistance, Qup = ultimate bearing capacity of pile
Skin friction → Caused by relative settlement of Pile
Negative Skin friction → Caused by relative settlement of Soil
I). Static formula
Qu = Qb + Qf = Bearing + Friction
Qb = qb Ab
Qf = qs As = αCAs ← Skin friction capacity of pile
Base area(Ab) = a² = Ab = π/4D²
Surface area(As) = 4aL = 2(a+b)xL = πDL
Safe load = Qf/FOS
End bearing pile → qu ∝ D²
Piles in Clay
Qu = Cub Nc Ab + α Cus As = 9NcAb + α Cus As
Nc = 9 (As per Skempton, Meyerhoff)
Adhesion factor (α) → very loose clay = 1, very stiff clay = 0.3, drilled piers on clay = 0.4
Friction Piles
Qu = Qf = qs As = αCAs
Safe load = Qu/Fos
ii). Dynamic formula
Best suited for Coarse grained soils
Underestimate the capacity where in localised momentary liquefaction takes place while driving the pile
Engineers New Formula
Q = WH/FOS(S+C)
Where FOS = 6, W = load in kN, H = ht of fall in cm, S = Settlement per blow in cm
Empirical factor(C) → Drop hammer = 2.5cm, Single acting steam hammer = 0.25cm
Modified Hiley Formula
Ultimate Driving Resistance → R = (WHη)/(S + C/2)
Most comprehensive of the pile driving formula
Group Action of Piles
Qg = α Cu Afg = η x n x Qu
Afg = (nS+D) x 4L = (3S+D) x 4L
min no of pile = 3 but for bored pile = 1
Pile caps → for spreading vertical and horizontal loads to all piles
Efficiency of pile group
η = Qug / n Qu
Group efficiency > 100% → C-less (Sand),
Group efficiency < 100% → C-Soil (Clay), Friction Piles
Efficiency Depends on → soil type, pile spacing, method of pile installation
Pile load Tests
To obtain → Modulus of subgrade reaction, Load settlement curve of a soil at a particular depth
initial test → To check the settlement at working load or to asses the allowable load
Routine test → On working piles for checking the settlement under working load
Minimum piles → initial = 2, Routine = 0.5 - 2%
Allowable/safe load on single pile = Minimum of 50% load corresponding to i) a settlement of 10% pile dia ii) a settlement of 25mm
Pile load test in compression → Total weight = 10% greater than the anticipated maximum test load
Load arrangements → Gravity loading platform, Reaction truss method
Types of pile load Tests
i. Pull-out test
Tension capacity of a pile
ii. Lateral load test
Lateral load capacity of a vertical pile
iii. Cyclic pile load test
To determine → Skin firctⁿ Resistance and base resistance separately, Point bearing load, Dynamic shear modulus of the soil
iv. Pressure meter test
To determine → Stress - Strain relationship of in situ soil, Elastic constants
Used for hard clay & dense sands
Under-reamed pile
To restrict damages due to volume changes of swelling soils
3-6m depth
Expensive soil(bcs), Soft soil with filled up ground
These are Bored piles
Shaft dia/Bulb dia = 1/2.5 = 0.4 → Db/Ds = 2.5
Bearing capacity → Double under reamed/Single under reamed = 1.5
Multiple bulb under-reamed pile → Expansive soil deposit, Multi storey building
Connected by reinforced beam known as grade beam
Grillage foundation
It is a Spread foundation
Heavy load on low bearing soil
I-sectⁿ → heavily loaded isolated column, 2 sets of perpendicularly placed steel bars
Design criteria for foundation for reciprocating type machine
Natural frequency ≥ 40%
Amplitude ≤ 0.2mm
Pressure within permissible limit
Max pressure due to static load = 0.4 x safe bearing capacity
Caisson or Well Foundation or Pier foundation
Deep foundation generally provided below water level for Bridges
Pier foundation → Suitable for underwater structure
Use → Bridge piers, River abutments, Dams
Grip length → Railway bridge = 50% max scour depth, Road bridge = 30% max scour Depth
Greater skin Friction retards sinking of Well
Tilt of well = 1 in 60
Floating caissons → Less expensive than Open caissons, Loads are not very heavy, Bearing stratum is at a shallow depth
Open caisson → Open both at top and at the bottom
Pneumatic caissons → preferred in situation where the soil flow into the excavated area is Faster than it can be removed
Dolphin → a type of Caisson
Box caissons → Emergency condition where time for sinking of caissons is not available
Shapes of Caisson or well foundation
Circular → D ≤ 9m
Double D wells → Abutment of bridge
Rectangular → Depth = 7-8m
Double octagonal wells → Bending stress are reduced, great Resistance to sinking
Settlement analysis of pile group
Settlement → individual pile > Group at same loading
Load is assumed to be transferred at angle of 30 degree
Pile group in clay → Equivalent raft method
VERTICAL STRESSES
a). Due To Concentrated Load
i. Boussinesq’s stress distribution theory
Assumption → isotropic soil, homogeneous, semi-infinite & elastic, soil is initially unstressed, hooke's law is valid, elastic medium, self wt. of soil is neglected, Distⁿ of vertical stress about VA is symmetrical, Change in Vol of soil due to load is neglected, soil below concentrated load,
used in engineering problem
Newmark's chart is based upon it
vertical normal stress → σ z ∝ 1/z²
σ z = 3Q/2πz²(1/(1+(r/z)²))^5/2
σ z = 0.4775Q/z² ← Exactly below Concentrated point load (r = 0)
If poisson’s ratio changes → No change in Vertical stress
If r/z > 1.524 → σ z westergaards > σ z Boussinesqs
If r/z < 1.524 → σ z westergaards < σ z Boussinesqs
ii. Westergaards eqⁿ
Assumption → Non-isotropic soil, Homogeneous, Elastic , Stratified soil layer*, layered soil, Poisson ratio = 0, Point load on the surface, Cohesive or Clay soil.
Results are more close to field
The Fenske chart is based upon it.
2:1 Method of stress under foundation
σ z = qLB/((B+z)(L+z))
Foundation base = BxL
q = Load/LB → Load = qLB
Newmark's influence chart
To determines stresses in soil due to surface loading
Based on Boussinesq eqⁿ
Vertical stress of any Shape Area or Loaded area of any shape
σ = qN/mn (q intensity of load, N equivalent no of area)
influence factor (IF) = 1/mxn = 0.005
IF = 0.8 for circular rigid footing
n = No of radial lines = 20 ← Generally
m = No of concentric circle = 10 ← Generally
Loaded area is drawn at scale = The depth scale shown in the chart
b). Approximate methods
i) Trapezoidal m
ii) Equivalent load m
iii) Stress isobar method → Zone of influence = 20% of load applied or Stress isobar
Isobar
Curve which joins points of equal vertical stress
20% isobar means → Vertical stress = 20% of load applied
Isobar can be prepared by boussinesq stress distribution theory
As depth of stress isobar increases → intensity of stress decreases
STABILITY OF SLOPE
Assumption Stability Of Slope → Shear parameters are constant, Slope stability problem is 2-Dimensional problem
Angle of repose → Max angle of inclination of the plane (with horizontal) at which a body remains in equilibrium under the action of friction
Mobilised shear strength means Applied shear stress
Stability of slope is decreased by →
a). Stability of infinite slope
FOS = τf/τ = (C + σ tan ϕ)/(γZcosβsinβ)
σ = γZcos²β
for C- ϕ soil → FOS = (C + γZcos²βtan ϕ)/(γZcosβsinβ)
for C-less soil → FOS = tanϕ/tanβ
for C-Soil → FOS = tanϕ/tanϕm = C/(γZcosβsinβ) = C/Cm = Hc/H → Hc = 4C/γ √Ka
Critical height of slope(Hc) = C / γ cos²β(tan β - tan ϕ), (taking Z = Hc, FOS = 1)
β = Slope angle(°), ϕ = Angle of internal friction(°), C = cohesion value (KN/m²)
Clay → β can be Greater than ϕ
Stability number → Sn = (tan(i)-tan(ϕ))cos²(i)
b). Stability of finite slope
i. Swedish Slip circle method
Purely cohesive
The surface of the sliding is assumed to be an 'arc of circle'.
Used to determine the Stability of the formation Slope railway line
Base failure → Soil below the toe is soft, weak & slope is flat, Depth factor > 1
Slope failure → Either Face or Toe failure, actual movement of soil mass
Face failure → soil close to the toe is quite strong, DF < 1
Toe failure → most common mode of failure, DF = 1
ii. Taylor stability number
Based on mobilised angle of shearing resistance
Sn = C/ γ Hc = C/ γ Fc H
Hc = FOS x H
Factor of safety(Fc) → Max depth of stable excavation = 1
max theoretical value = 0.5
max practical value = 0.261 for clay ( ϕ = 0 )
Taylor's stability chart are based on the total stress using Friction circle method
Angle used for shearing resistance = mobilised angle
iii. Friction circle method
Assumption → Resultant force on rupture surface is tangential to circle
Friction circle radii → r = Rsinθ
iv. Fellenius method
For purely cohesive soil
method of slice → 1st suggested by Fellenius
Critical centre → lie at the intersection of Directional angle
Bishop’s simplified method of slice
Assumption → Slip surface as an arc of a circle, resultant interslice shear force is zero
Disregards the effect of the forces acting on the sides of the individual slices.
Applicable for Homogeneous soil
SOIL EXPLORATION & STABILISATION
Clear working space at bottom of soil exp Pit → 1.2 x 1.2 m
Undisturbed sample → Size distribution, Atterbergs limits, Consolidation parameters, Coeff of permeability, shear strength parameters, Density.
Disturb sample → All lab tests & tests on sand, ex. Specific gravity, Grain size, Plasticity characteristics
Soil sampling boreholes should be stabilised for prevention of collapse of side walls of borehole
Swelling pressure = maximum force/Area
Significant depth
Depth up to which increase in pressure due to loading is likely to cause perceptible settlement or shear failure
Ds = 0.2q → q = intensity of loading
Depth of exploration = 1.5 x width of footing
Method of Boring
Auger boring → Partially saturated sands, silts & medium to stiff Clays
Wash boring → Not for hard soil
Percussion boring → Boulder & gravelly stratum
Rotary Boring → Mud rotary Boring
i. inside clearance
Ci = (D3 - D1) / D1
Range = 1 - 3%
ii. Outside clearance
Co = (D2 - D4) / D4
Range = 0 - 2%
iii. Area ratio
Degree of disturbance for a soil sample collected from sampler
Ar = (D2² - D1²) / D1²
Range = 10 - 20%
To minimise sampling disturbance → Ar = 1 = 100%
Stiff clay or formation < 20%
Sensitive clay < 10%
Undisturbed sample < 10%
Thin wall sampler < 8%
iv. Max t of cutting edge
t = (D2-D1)/2
use Ar = 0.2(20%) to find D1.
v. Recovery Ratio
RR = L/H = Recovery length/Penetration length = Length of Sample before withdrawal/Penetration of the sampler in the soil mass.
Good recovery/soil = 1
Compressed soil (Shrink) < 1
Swelled soil > 1
Sampler
Split spoon sampler → most commonly used for disturb sample
i. Open drive Sampler
Thin wall sampler & Shelby tube → Used for undisturbed soil samples, Ar <10 %
Thick wall sampler → Disturb sample but representative samples, Ar = 10 - 25%
ii. Stationary piston sampler
Undisturbed sample of soft, Sensitive clays, Saturated sands
iii. Rotary sampler
Bulk samples of large size such as stiff soils, hard cohesive soil & stones rocks.
Soil Stabilisation
To increase strength & stability of soil
Lime Stabilization of soil
Hydrated Lime Ca(OH)2 → Use for Plastic clay soil
Most effective for Black cotton soils, wet cohesive soil, moderate to high plasticity
improve the strength, stiffness & Durability of fine-Grained Clayey soils
increase in Lime content causes reduction in Swelling pressure → thus increase in Shrinkage limit & Plastic limit
Lime required for stabilisation = 3 - 8 % of expensive soil
Plasticity increases → Required quantity of lime increases
Leads to → Flocculation of particles, LL↓, PL↑, SL↑, Swelling ↓, Plasticity index ↓, max dry density ↓
Cement stabilisation
Bitumen stabilisation
Suitable for Sandy soil
Imparts cohesion and reduce water absorption
DOSE
Liquification : Sand loses its shear strength due to oscillatory motion
open caissons are less expensive than floating caissons.
Shelby tube : collecting undisturbed soil sample
Hygroscopic water: driven off by heat
Oedometer: compressibility
Odometer: Vehicle
Plastic equilibrium: verge of failure
Nuclear density Gauge: moisture content & wet,dry density.
Dense sand: high bearing capacity
Quick sand: Seepage pressure
wet stenting: a type of particle size test.
Poiseuille: flow through capillary
porosity ↑es : aquifer yield large vol of water
Sonoscope: direction of leakage (underground water)
Lime stabilisation is used for clay soil.
SPT: bearing capacity
Hydrometer : grain size analysis
Proctor : compaction
Vane test : shear strength
Meyerhoff Theory: no Water table correctⁿ
Sediment transport → Soil is assumed as incoherent
No comments:
Post a Comment