Surface Investigation
Area ratio for sampler = x 100%
Inner clearance = x 100%
Outer clearance = x 100%
Where, D2 is outer diameter of cutting edge.
D1: Inner diameter of cutting edge D3: Inner diameter of sample tube D4: Outer diameter of sample tube.
Area ratio should be as low as possible
Sounding tests are used to measure penetrative resistance.
For SPT, first 150mm settlement is taken as redundant
If N>15 in SPT, corrected Ne = N + (N – 15)
In SPT, dilation correction is Ne = N * +
Where σ is effective overall under pressure.
In cone penetration method, resistance profile for first 8cm of penetration is recorded.
In electrical reactivity method, resistivity = 2ΩD R Where R = Resistance
D = Spacing between electrodes.
Earth Pressure
In active state, retaining wall moves away from the soil wedge.
Active pressure = vertical pressure Where,
= =
tan ( )
= sin sin
= Co-efficient of earth pressure
In passive state, retaining wall moves towards the soil wedge and resistance acts downward.
KP= , = tan ( )
KP: Coefficient of earth pressure (passive) for C = 0 soil.
When the wall is at rest =
K0= ,
K0: Coefficient of earth pressure at rest.
In no submerged condition pressure active, Pa = x x H2
In submerged condition, Pa = x x H2 + x x H2 Back fill with uniform surcharge
Total active pressure
=2 Where q is the surcharge
In code of surcharge, total active pressure = ∫ z q
Back fill with sloping surface
Ka = Cos β* √ + √
KP = Cos β* √ + √
If back fill is submerged, P = √ where P1 = x Ka x r x H2
In case of cohesive backfill Pa = rH2 Cot2∝2- 2C Cot ∝ H PP = rH2 Tan2∝2 + 2C tan ∝ Where ∝ = ( )
In active case, cohesive soil should be able to withstand the depth of tan ∝.
Depth of tension crack = tan ∝.
φ angle = - - δ where δ is angle of indication of Pa and normal of wall.
Stability of Slopes Types of Slopes Infinite Slope
A representing the boundary surface of a semi infinite soil mass and having soil properties uniform at every depth
Finite slope: A slope of limited extended Factor of safety =
Where = Shear strength
=Shear stress acting on the soil
For cohesive soil & non cohesive soil generation formula for factor of safety is FC =
+
If water table / seepage is not present.
For C = 0 (i.e., for cohesion loss soils) FC =
If seepage is parallel to the slope FC =
If submergence in a certain portion of slope
If seepage is parallel to the slope
= C
cos i sin i
.tan tan i Again for cohesion less soils C= 0 =
.tan tan i
If the slope is submerged
=C cos i tan cos i sin i For cohesion less soils
=tan
tan i. e. , same as in dry state
If su mergence in a certain potential =*
+ tan tan Where Z = Total height of slope
h = Height of slope above i = Angle of slope
= Angle of internal friction C = Cohesion of soil
Critical height of any slope can be found by putting = and = in then the formula for as applicable
E.g.: critical height of a submerged slope of cohesive soils
= tan tan cos
Stability number =
= Sn
= FC
Where is called the mobilized cohesion
= Sn
Depth factor , Df =
Where, H = Height of slope
D = Depth of soil between slope and hard strata.
FC =
̅ for = soil.
Where , x̅ = Distance of centroid of slip circle from centre of rotation r = Radius of slip circle.
For C - soil.
FC =
Where N is sum of normal components of weight is with respect to tangent of slip circle T is sum of tangent components of weight along slip circles.
Culman method assumes wedge / planar failure.
Swedish method assumes circular failure.
Types of Foundation
Raft footing
Allowable differential settlement = 65 to 100mm on clay.
On sand : 40 to 65mm.
Definitions
1. Bearing Capacity
The load or pressure developed under the foundation without introducing any damaging movement in foundation and in the supported structure, is called bearing capacity of solid.
2. Gross Pressure Intensity
It is the total pressure at the base due to weight of the super structure 3. Net Pressure Intensity
It is defined as the different in intensities of the gross pressure after the construction of the structure and the original over burden pressure
If D is the Depth of footing q = q - σ = q – r D
4. Ultimate Bearing Capacity
It is the minimum gross pressure intensity at the base of foundation at which the soil fails in shear.
5. Net Ultimate Bearing Capacity (qnf)
It is the minimum net pressure intensity causing shear failure of soil q = q + σ
6. Net Safe bearing Capacity
The net safe bearing capacity is the net ultimate bearing capacity divided by a factor of safety F
q =
7. Safe bearing Capacity
The maximum pressure which the soil can carry safely without rest of shear failure is called safe bearing capacity
q = q + rD = + rD Types of failure of foundations
General shear failure occurs in stiff soils.
Local shear failure soil with single compressibility and sands.
Footings at very shallow depth in loose sand are susceptible to punching failure.
Angle of zone III in Terzaghi analysis is 450 – with horizontal.
For a strip footing
qf = CNC + σ̅ Nq + 0.5 r BNr
For bearing capacity factor , and depends only
= a
where a = e( . )
= ( ) cot
=tan
2 (
cos )
Where = passive earth pressure coefficient dependent on , , are also given in standard tables
For qs = ( σ̅ σ̅ . r r )+ σ̅
Whereσ̅ = .
Terzaghi’seqn for local shear failure.
(C =2
C) and tan =2 tan
qu = CNC + σ̅Nq` + r BNr`.
Guidelines for Local Shear Failure Condition for Shear Failure (i) Stress strain test (l- soil)
General shear failure→ low strain < % Local shear failure → strain of to 2 % (ii) Angle of shear resistance
Φ > , general shear failure Φ <2 , local shear failure (iii) Penetration test
≥ : general shear failure ≤ : local shear failure (iv) Plate load test
Shape of the load ‘settlement curve decides whether it is general shear failure or local shear failure
(v) Density Index
I > 70, General shear failure I < 20, Local shear failure
or friction cohesive soil →
qf = 1.3CNC + qnq + 0.3 NrBr for circular footing
For square footing, qf = 1.3 CNC + qNq + 0.4 rBNr
For rectangular footing, qf = 1.0 CNC*( . )+ + qNq + 0.5 rBNr* .2 +
For local failure (or local shear).
Cn = C
Tan m = Tan m.
Nq = Tan2( )r Tan .
NC = (Nq– Cot .
Effect of water table on bearing capacity is taken by, RW1& RW2
qf = CNC + qNq x RW1 + 0.5 Nr x B x r2 x RW2.
RW1 = 0.5 * +
RW2 = 0.5 * +
Where ZW1 = Depth of water table from surface or ground level.
ZW2 = Depth of water table from base of footing.
Max RW1& Max RW2 = 1
Effect of size of plate in settlement on granular…. soil: = * * . . + Where δ : Settlement of footing
δ : Settlement of plots.
For clayey soil
∫
∫ = * +
Total settlement of footing is S = Si + SC + SS
μ = Poison ratio
Es = Modulus of elasticity
Iw = 0.88 – 1.70, 0.88 for rigid circular footing and 1.70 for rigid rectangular footing.
B = Least dimension of footing.
SC = H x CC log10( )…
CC : 0.009 (WL – 10) L0 : Initial void ratio
C : Coefficient / correction factor depending upon geometry of footing and history of loading on clay.
Es : * +
CC = 0.007 (WL – 10) for remoulded sample.
Pile Foundation
Pile driving is done by drop hammer, single acting hammer, double acting hammer and vibratory hammer.
Dynamic formulae
Engineering news formulae
1. Drop hammer, Qa = Where S : final set per blow.
C : 2.5 cm for drop hammer.
2. Single acting steam hammer Qa = .
3. Double acting steam hammer Qa = .
a = area of piston p = pressure of steam.
Hiley’s formulae Qf =
nb = if W > iP
nb = * + if W < iP.
In case of submerged loose soil equitation may take place due to dynamic load.
Use of dynamic formulae for clay is meaningless.
Static formulae Qmp = Rf + RP.
= As rf + Aprp. rf: Average spin function rp: Point function
As: Surface area Ap: Point area.
For cohesive Clay rf = αC̅ (or mC̅
rp = 9Cp
Qmp = mC̅Ap + 9CpAp.
For non cohesive soil rf = Tan rz q rp = 0.3 rBNrq [for circular]
rp = rBNrq [for rectangular]
In clayey soil, group efficiency of function piles may be less than sum of individual efficiencies of pile.
In end bearing piles, group efficiency = n x individual efficiency Where, n = number of piles.
Converse labre formula.
ηg = 1 -
*
+
= Tan–1( )
where, m: number of piles in a row n: number of rows.
d: diameter of pile
s: spacing (C/C) between 2 piles.
Settlement of pile group in clay δ =
logi( )
where, H = height of clay strata e = initial void ratio
One – third height of pile will also contribute in load transfer.
Angle of load dispersion may be assumed to be 300. Qu =Ap x NC x Cb + Aa + NC x Ca Ca x As ∝Ca As.
Ap : Cross section area of pile stem at soil.
NC: Bearing capacity factor = 1
CP: Cohesion at tos of pile
Aa = u , where Du is dia. of underream, D is diameter of stem.
Ca` = Average cohesion of soil around underream drills.
As` = Surface area of cylinder curricumscriling under-reams.
Ca = Average cohesion of soil along pile stems.
Cu = for clayey soil.