KNS_LRFD-GEOTECH_CHANGA_08-09-21-RKS.pdf

LOAD & RESISTANCE FACTOR DESIGN
FOR GEOTECHNICAL ENGINEERING PROBLEMS:
(NEED FOR RATIONALIZATION)
K. N. SHETH
CIVIL ENGINEERING DEPARTMENT
DHARMSINH DESAI UNIVERSITY
NADIAD
SEPEMBER 2021
1

2
• Structural Design Philosophy and implementation to Codes of Practice has
transformed from conventional Working Stress Method (WSM) using FoS to
Limit State Method (LSM)
• Working Stress Method: To attain Margin of Safety, Material Strength is
divided by a FoS to equate with Working Loads.
RCC design, IS 456 – 1964: Conc. FoS = 3 for flexure & 4 for Compression
Reinf. FoS = 1.70
Steel Structures, IS 800 - 1984 : FoS = 1.7
Introduction:

3
• Limit State Method for RCC Structures is implemented (IS 456: 1978) using
Partial Safety Factor approach. Inplace of FoS, two Safety Facotors are used:
for Loads & Materials, Table 18 : IS 456-2000:
•Partial safety factors for Loads: (Multiplier)
Introduction:
Load
Combination
Limit State of Collapse Limit State of Serviceability
DL IL WL/EQ DL IL WL/EQ
DL + IL 1.50 1.50 1.00 1.00
FL+WL/EQ 1.50 1.50 1.00 1.00
DL+IL+WL/EQ 1.20 1.20 1.20 1.00 0.80 0.80
Partial safety factors for Materials: (Strength Reduction Factors)
Concrete 1.50 (for Cube Strength) , Steel Reinforcement : 1.15
• Load and Resistance Factor Design (ACI - 318) for RCC Structures:
Three Partial Safety Factors: Loads, Materials & Resistance Calculations

4
Design Methods : Structural Engineering
• Design Criteria:
− Stability : against global failure (failure of support system )
▫ Overturning, Sliding (Attained by Global proportioning)
− Safety : Collapse due to inadequate strength
Maximum Stress < Strength (Collapse State)
− Serviceability : Deflection, cracking, Vibration
Assessed for behaviour under Working Load (Service State)
− Durability : Resistance to natural forces during life cycle
(Attained by Material Specification & Detailing)
• Main Objectives of Structural Design:
1. To attain margin of safety against collapse state
2. To assure a functional structure in service state

5
Structural Analysis: To Calculate
− External Reactions
− Internal Forces
− Internal Stresses
− Strains
− Deformations/Deflections
Type of Problems:
• Framed Structures
• Planar Structures
− Slabs
− Shear Walls
− Folded Plates, Shells
• Analysis Methods :
− Elastic Analysis
− Plastic Analysis
− Nonlinear
Elastoplastic Analysis
• Design Methods:
a) Working Stress Method
b) Ultimate Load Method
c) Limit State Method :
2 partial safety factors
d) Limit State Method : (LRFD Method)
3 partial safety Factors

6
Variation of +ve BM in Midspan
due to choice of Analysis Method

7
• Structural Design - Steps:
− Define Structural System, Base fixed / hinge
− Select Materials : Strength Deformation parameters
− Proportioning members (approx.)
− Load estimate and load combination
− Analysis results : Axial, Shear Force, Bending
Moment, Torsion
− Member design to satisfy design criteria
− Detailing
By iteration

8
• Design Problem: Design of benches
• Data : L= 2m, b = 50cm, yield stress 𝑤𝑜𝑜𝑑 𝜎𝑦 = 150 kg/cm2
• 4 persons of 75 kg each = 75 * 4 = 300 kg (Self weight is neglected)
• Idealized UDL = 300 kg / 2 m = 150 kg/m
◦ Internal forces, Mmax =
150 ∗22
8
= 75 kg.m, Vmax= 150 kg
◦ 𝑀𝑅 = 𝜎𝑦 * Z  Z =
75 ∗100
150
= 50 cm3
◦ Hence,
𝑏𝐷2
6
= 50. Therefore, D = 2.45 cm.
75 75 75 75
150 150
2m

9
Uncertainties involved in the problem
1. Loadings
− Dead Load : ± 10 to 20 % variation
− Live Load : 50 to 60 %
2. Material
‒ Strength : (wood : 30-35 % variation)
‒ Geometry : Marginal
 in length
 In cross section
3. Resistance calculation methods
‒ Theory of pure bending is used
‒ Small Deflection theory is used
‒ Linearly Elastic model is used

10
1. Loadings
− Dead Load : ± 10 to 20 % variation
− Live Load : 50 to 60 %
2. Material
‒ Strength : (wood : 30-35 % variation)
‒ Geometry : Marginal
 in length
 In cross section
3. Resistance calculation methods
‒ Theory of pure bending is used
‒ Small Deflection theory is used
‒ Linearly Elastic model is used
Margin of Safety
for Overload
Margin of Safety for
Under- Strength
Margin of Safety for
Simplified analysis
method

11
• Safety has to be ensured with uncertain inputs/outputs of varying degree.
• To assure safety, evaluate reliability of all uncertainties in Design
process.
• Mathematically, Reliability Theory : Level – 3 is best to define level of
safety
• It gives probability factor for failure as
Pf = 10−6
, 10−7
etc. that is 1 in 1,000,000 or 1 in 10,000,000
• In Civil Engineering, first structures are evolved by experience and
expertise of engineers – Empirical Method
• Then methods are formulated
• Then methods are proved on Mathematical Tools (e.g. FEM)

12
To cater safety with respect to
• Loading
• Material
• Strength Calculation Methods
Earliest design method is Working Stress method :
• Margin of safety is provided by Factor of Safety to σy
• FoS = 3 for general problems
• So 𝜎𝑎= 𝜎𝑦/FoS = 50 𝑘𝑔/𝑐𝑚2
• Hence, Z =
𝑀
𝜎𝑎
=
75 ∗100
50
= 150 cm3
• Hence,
𝑏𝑑2
6
= 150. Therefore, D = 4.24 cm

13
Ultimate Load method :
• Margin of safety is provided by load factor to the Loads (λ)
• We= λ * W ; λ = 1.7 to 2
• For λ = 2, Mu=2 ∗75= 150 kg.m
• Hence, Z =
𝑀𝑢
𝜎𝑦
=
150∗100
150
= 100cm3
• Hence,
𝑏𝑑2
6
= 100. Therefore, D = 3.46 cm

14
Working Stress Method
• Margin of Safety with reference to
material only
• Loads with variable uncertainty
are treated at par
‒ DL = 10 to 20 %
‒ LL = 50 to 60 %
• Margin of Safety with respect to
material strength is not cognizable.
Ultimate Load Method
• Margin of Safety with reference to
loads only
• Different margins can be assigned
to DL and LL
‒ 𝜆𝐷𝐿= 1.3 to 1.7
‒ 𝜆𝐿𝐿= 1.5 to 2.0
• Margin of Safety with respect to
load imparts physical sense and is
preferred.
Have same
margin

15
• Design stress level much lower
than collapse state, nonlinearity can
be ignored.
• Designed at collapse state so
nonlinearity of stress-strain need to
be considered. Hence, calculations
are complex.

16
• Design stress level much lower
than collapse state, nonlinearity can
be ignored.
• Analysis method and design
approach both consider linear
elasticity.
• As design is at service state,
serviceability criteria is also
verified.
• Designed at collapse state so
nonlinearity of stress-strain need to
be considered. Hence, calculations
are complex.
• Structural Analysis is done by
Linear Elastic method whereas
Design is done considering
Nonlinear, collapse state
• Designed at collapse state so check
for deflection etc. at service state
required.

17
Limit State Method :
• Main Limitation of
‒ WSM : Margin of safety for material parameter only
‒ ULM : Margin of safety for loads only
‒ WSM : Design at service state only
‒ ULM : Design at collapse/ultimate state only
• An advanced method introduced with multiple safety factors applied to
material parameters and loadings partially

18
Multiple State Design
‒ Limit state of collapse (ULS) {Non-linear behavior}
‒ Limit state of serviceability (SLS) {linear behavior}
• Thus , it caters the need to have
‒ Margin of safety for :
o Under Strength
o Over loads
‒ Assess the deflection and cracking etc. : serviceability (SLS)
ULS

19
• To define probability of failure zone : Level III Reliability analysis is
required.
• It gives Pf - Probability of failure for defined Risk

20
• Level II reliability is
• β =
ln(
𝑅𝑚
𝑄𝑚
)
𝑉𝑅
2+𝑉𝑄
2
• Where 𝑉𝑅 =
𝜎𝑅
𝑅𝑀
and 𝑉𝑄 =
𝜎𝑄
𝑄𝑀
;
σ = Standard Deviation
• Reliability Index = σ *β indicates Difference of mean value to failure

21
• β Pf
• Evaluation of β requires extensive data of test results and loading studies
as well.
• In Limit State Method, Level – I reliability method is used.
• That is, by defining
‒ Characteristic loads
‒ Characteristic Strength
β 2.32 3.09 3.72 4.72 4.75 5.2 5.61
Pf 10−2 10−3 10−4 10−5 10−6 10−7 10−8
5 % probability accepted

22
• Probabilistic approach are defined to arrive at
‒ Service loadings : Characteristic loads
‒ Material Strength : Characteristic strength

23
• Limit State Method : Two partial safety factor Approach
‒ Partial safety factor for loads (γf) 𝑄𝑑 = 𝛾𝑓 * 𝑄𝑐ℎ
‒ Partial safety factor for material strength (γm) 𝜎𝑑=
𝜎𝑐ℎ
𝛾𝑚
• For RCC Design,
‒ γm = 1.50 for concrete on cylindrical strength = 2.25 for cube strength
‒ γm = 1.15 for reinforcing steel
◦ γf for different load combinations
Combination
γf (ULS ) γf (SLS )
DL IL WL/EQ.L DL IL WL/EQ.L
DL + IL 1.5 1.5 - 1.0 1.0 -
DL + IL +WL/EQ.L 1.2 1.2 1.2 1.0 0.8 0.8
DL+WL/EQ.L 1.5 - 1.5 1.0 - 1.0

24
• Resistance is proportional to Strength
‒ Nominal Resistance
𝑅𝑛
𝛾𝑚
= Qch x γf =>
𝑅𝑛
𝑄𝑐ℎ
= 𝛾𝑚* 𝛾𝑓
• A crude comparison with WSM :
• FoS =
Nominal Resistance
Design service loads
=
𝑅𝑛
𝑄𝑐ℎ
= 𝛾𝑚 * 𝛾𝑓
= 2.25 * 1.5 (DL + IL) = 3.375
• FoS for WSM = 3
• For DL +IL +WL combination (σ is increased by 33 %)
‒ WSM : FoS = 3 / 1.33 = 2.56
‒ LSM : FoS =
𝑅𝑛
𝑄𝑑
= 𝛾𝑚 * 𝛾𝑓 = 2.25 * 1.2 = 2.70
With reference to
Concrete only

25
• In Limit State method for Steel, material partial safety factors
‒ Resistance governed by Yield, γmo
= 1.10
‒ Resistance governed by Ultimate Stress, γm1 = 1.25
Rn
γm
≥ Qf ∗ γ
f
‒ FoS = γmo * γf = 1.10 * 1.50 = 1.65 (Yield governs)
‒ FoS = γm1 * γf = 1.25 * 1.50 = 1.875 (Ultimate stress governs)
‒ Yielding governs for gross sections, σy = 250 MPa
‒ Rupture governs for critical sections, σu = 410 Mpa
Thus, WSM imparts Simplicity in concept and application

26
• ACI 318 format is 3 Partial Safety Factors format
Loads Material Strength
γf γm Sd= ɸ ∗S
Flexure – 0.9
Axial Compression - 0.7
Shear/Torsion – 0.85

27
GEOTECHNICAL ENGINEERING : DESIGN APPROACH
•In India, IS 6403 provides guideline to calculate ultimate bearing capacity
for shallow foundations.
•It gives bearing capacity factors and other factors viz. inclination factors,
depth factors, shape factors etc.
•To calculate allowable bearing pressure a FoS of 2.50 is recommended.
GEOTECHNICAL DESIGN

28
Continuous efforts are made to
transform Geotechnical Design
Philosophy for implementation of
Load and Resistance Factor Design
(LRFD) in place of conventional
WSM. Eurocode-7 accommodates
this Limit State approach since 1995
for Geotechnical Engineering.
GEOTECHNICAL DESIGN

29
IRC is in the process of evolving
Guidelines based on EC-7 in this
context for design of foundations
for Bridges – IRC 78. It includes
Shallow Foundations, Pile
Foundations, Retaining Walls etc.
GEOTECHNICAL DESIGN

30
• For Design of RCC Beam :
Factored Moment of Resistance is calculated as
Mu = 0.87 𝑓𝑦 𝐴𝑠𝑡 𝑑 1 −
𝐴𝑠𝑡 𝑓𝑦
𝑏 𝑑 𝑓𝑐𝑘
: γm = 1.50 for conc., 1.15 for steel
Material properties are directly used in the calculation of Resistance
• For Design of Shallow Foundations:
Ultimate Bearing capacity is calculated as
qult= 𝑐. 𝑁𝑐. 𝑠𝑐. 𝑖𝑐. 𝑑𝑐 + 𝑞. (𝑁𝑞−1). 𝑠𝑞. 𝑖𝑞. 𝑑𝑞 + 0.5 𝐵. 𝛾. 𝑁𝛾. 𝑠𝛾. 𝑖𝛾.𝑑𝛾. 𝑊′
Material properties c and Φ are not directly used in the calculation of
Resistance. Based on ‘Φ’ indirect parameters (Nc, Nq, N𝛾) are used.
Moreover, Resistance depends on Type of Failure determined based on
‘Φ’.
Hence, implementation of Partial Safety factor for Material is not so
simple as in Structural Design.

31
The Ultimate Net Bearing Resistance as per IS 6403:1981 is calculated as:
1) For General Shear Failure
qult= 𝒄. 𝑵𝒄. 𝒔𝒄. 𝒊𝒄. 𝒅𝒄 + 𝒒. (𝑵𝒒−𝟏). 𝒔𝒒. 𝒊𝒒. 𝒅𝒒 + 𝟎. 𝟓 𝑩. 𝜸. 𝑵𝜸. 𝒔𝜸. 𝒊𝜸.𝒅𝜸. 𝑾′
where design Dimensionless factors are
𝑁𝑞 = 𝑒𝜋 .tan 𝜙
. 𝑡𝑎𝑛2
45 + 𝜙′
/2
𝑁𝑐 = 𝑁𝑞 − 1 cot 𝜙′
𝑁𝛾 = 2 𝑁𝑞 + 1 tan 𝜙′
Design of Shallow Foundations: WSM

32
2) For Local Shear Failure
qult= 0.67 𝑐. 𝑁𝑐′. 𝑠𝑐. 𝑖𝑐. 𝑑𝑐 + 𝑞. (𝑁𝑞′ − 1). 𝑠𝑞. 𝑖𝑞. 𝑑𝑞 + 0.5 𝐵. 𝛾. 𝑁𝛾′. 𝑠𝛾. 𝑖𝛾.𝑑𝛾. 𝑊′
Use 𝜙′
= 𝑡𝑎𝑛−1
(2
3 𝑡𝑎𝑛∅) to calculate design factors
Type of Footing 𝑠𝑐 𝑠𝑞 𝑠𝛾
Continuous Strip 1.0 1.0 1.0
Rectangle 1 + 0.2 B / L 1 + 0.2 B / L 1 - 0.4 B / L
Square 1.3 1.2 0.8
Circle 1.3 1.2 0.6
Shape Factors:

33
- The Depth Factors of Foundation
𝑑𝑐 = 1 + 0.2 𝐷𝑡/𝐵 . 𝑁𝜙
𝑑𝑞= 𝑑𝛾= 1 for 𝜙 < 10˚
𝑑𝑞= 𝑑𝛾= 1 + 0.1 𝐷𝑡/𝐵 . 𝑁𝜙 for 𝜙 > 10˚
where, 𝑁𝜙 = tan 45 + 𝜙/2
- The Inclination Factors
𝑖𝑐 = 𝑖𝑞 = (1 − 𝛼 / 90)2
𝑖𝛾= (1 − 𝛼 / 𝜙)2

34
Criteria for use of General Shear Failure & for Local Shear Failure :
(i) Cohesionless soil: Use Table 3 of the code, it is given below
◦ Relative Density > 70%, void ratio < 0.55 : General Shear Failure
◦ Relative Density < 30%, void ratio < 0.75 : Local Shear Failure
◦ Relative Density 20 to 70 %, void ratio 0.55 to 0.75 : Mixed Shear Failure,
(interpolate between General Shear Failure and Local Shear Failure)
(ii) Cohesive soil: Cl. 5.3.1.1 recommends use of general shear failure for all
the types of clays.

35
Guidelines Followed In Practice: Method of Analysis for given soil type is
selected based on type of soil and strength parameters as given in Table
below
1. For Cohesionless soil
Method of
Analysis
Relative
Density
Φ° (Lab
Test/ based
on SPT)
Corrected
SPT N-value
(Field Test)
Void Ratio
General Shear >=70 % >=36 >= 30 <= 0.55
Mixed Shear 20 % to 70 % 29 to 35 10 to 30 0.55 to 0.75
Local Shear < 20% <= 28 =<10 >0.75

36
For example, Mixed shear failure parameters for Φ = 32 are evaluated as :
Nq, m = N’q + [ (Nq –N’q) / 8 ] x (32-28)
Where N’q = 8.33 as local shear parameter for Φ =32
(Read for Φ =22.6°)
Nq = 23.18 as general shear parameter for Φ =32
Hence we get, Nq,m = 15.75 (Mixed Shear Parameter)
The effect of the decision can be seen with the illustrative problem.

37
Prob-1 : A 2m x 2m square footing is placed at 1m depth below ground level
in a homogeneous cohesionless stratum with Φ = 32, Unit weight of soil is
20 kN/m2. Ground water table is not encountered.
Method of Analysis
Net Ultimate Bearing
Capacity, kN/m2
Net Safe Bearing
Capacity, kN/m2
General Shear 1107 443
Mixed 717 287
Local Shear 327 131

38
Limit State Method for Geotechnical Engineering
• Design Problems in Geotechnical Engineering :
Ultimate State Service State
Shallow foundations √ √ (Settlement)
Deep foundations √ √ (Settlement)
Retaining Walls √ ×
Slope Stability of
Embankments
√ ×
Excavations √ ×

39
Evolution of Design Methods :
• Experiments, experience and learning from failures
‒ To check pile capacity – actual load test
‒ Based on experience gathered : Building codes gives Presumptive
Bearing Capacity ( e.g. NBC – India )
• Development of Empirical formulae :
‒ Terzaghi / Teng’s equations for N – value
‒ Correlations N - ɸ , N - Rd, N – settlement, N – SBC etc.
• Theoretical development using mathematical formulation and modifying
this to comply experience and experiments is evolution of Working
Stress Method.
e.g. implementation of bearing capacity for local shear failure.

40
Geotechnical Design Approaches:
• Design by Calculations
• Design by Prescriptive Measures
• Design by Actual Load Tests
• Design by Observational Methods
Geotechnical Categories:
1. Small and Simple Structures : Negligible Risk
2. Conventional Structures : No Exceptional Risk
3. Special Structures or Difficult Sub-Soil Conditions
EC7 defines Ultimate Limit States and Serviceability Limit States

41
BS EN 1997-1:2004
Eurocode 7: Geotechnical design
Part 1: General rules
◦ 12 sections
◦ Annexes A to J
◦ National Annex to Part 1
Part 2: Ground investigation and testing
◦ 6 sections
◦ Annexes A to X
◦ National Annex to Part 2

42
Ultimate Limit States: Where relevant, following limit states are not
exceeded:
• EQU : Loss of equilibrium of structure or ground, considered as a rigid
body, in which strengths of structural materials and the ground is
insignificant in providing resistance.

43
Ultimate Limit States:
• EQU
• UPL : loss of equilibrium of the structure or the ground due to uplift by
water pressure (buoyancy) or other vertical actions.

44
• EQU
• UPL
• HYD : Hydraulic heave, internal erosion and piping in the ground caused
by hydraulic gradients

45
• EQU
• UPL
• HYD
• STR : internal failure or excessive deformation of the structure or
structural elements, including e.g. footings, piles or basement walls, in
which the strength of structural materials is significant in providing
resistance.

46
• EQU
• UPL
• HYD
• STR
• GEO : failure or excessive deformation of the ground, in which the
strength of soil or rock is significant in providing resistance.

47
Fundamental Limit State Requirements :
Design/Factored Action Effect Ed ≤ Rd Design Resistance
Ed = E {Fd, Xd} = E { Fch * ϒF, Xch/ ϒM }
Fch = Characteristic Action/Force
Xch = Characteristic Material Strength parameters
ϒF = Partial Safety Factor for Action
ϒM = Partial Safety Factor for Material Strength
&
Rd = Rch / ϒR
ϒR = Partial Safety Factor for Calculated Resistance

48
Characteristic values of geotechnical parameters
• The selection shall be based on derived values resulting from laboratory and
field tests, complemented by well-established experience.
• The greater variance of c' compared to that of tan φ shall be considered
when their characteristic values are determined.
• The selection of characteristic values for geotechnical parameters shall take
account of the following:
− geological and other background information, such as data from previous
projects;
− the variability of the measured property values and other relevant
information, e.g. from existing knowledge;
− the extent of the field and laboratory investigation, type and number of
samples, the extent of the influence zone of ground.
− designer’s expertise and understanding of the ground

49
Characteristic Values in EC7 : Characteristic values of geotechnical
parameters

50
− Characteristic = moderately conservative = representative (BS8002) =
what good designers have always done.
− The characteristic value of a geotechnical parameter shall be selected as a
cautious estimate of the value affecting the occurrence of the limit state.
− If statistical methods are used, the characteristic value should be derived
such that the calculated probability of a worse value governing the
occurrence of the limit state under consideration is not greater than 5%.

51
Design of Shallow Foundations: EC7

52
R3 = R1=1.0 Hence DA1 C2 = DA3

53
DA1 C2 = DA3

54
• Eurocode 7 has standardize LRFD Method for Geotechnical Applications
L-M-R COMBINATIONS FOR SHALLOW FOUNDATIONS AS PER EUROCODE 7

55
Bearing Resistance, Rd
Vd < Rd,
Where, Vd is the design action which includes;
• Supported Permanent Load
• Weight of Foundation
• Weight of Backfill
• Loads from Water Pressure
• Uplift
* Analytical Method for Bearing Resistance Calculation also accounts for Drained as well
Un-drained Conditions

56
Sample Problem Confirming to Eurocode 7
A square pad footing of Length L = 2.0 m, breadth B = 2.0 m and depth Df
= 2.0 m
Permanent action VGK = 2000 kN
Imposed variable action V QK = 1000 kN, both applied at the centre
Angle of Shearing Resistance 𝜙k = 36˚
Effective cohesion c’k = 0 kPa
Weight Density 𝛾k = 18 kN/m3
Weight density of Reinforced Concrete 𝛾ck = 25 kN/m3

57
Design Approach: DA1-C1
Actions and Effects
Partial Factors A1 and A2 : 𝛾G = 1.35, 𝛾Q = 1.50
Design Vertical action V d = 𝛾G x VGK + 𝛾Q x VQK = 4200.0 kN
Area of base = Ab = L x B = 4.00 m2
Design Bearing Pressure = qEd = Vd / (LxB) = 1050.0 kPa

58
Material Properties and Parameters:
Partial Factors from M1 and M2 : 𝛾𝜙 = 1.00 , 𝛾c = 1.00
Design Angle of Shearing Resistance 𝜙 d = tan−1 tan 𝜙𝑘
𝛾𝜙
= 36˚
Design Cohesion = c’d =
𝑐′
𝑘
𝛾𝑐
= 0 kPa
Bearing Capacity Parameters
Nq = 37.75 Nc = 50.58 N 𝛾 = 53.40
Shape factors
Sq = 1.59 Sc = 1.61 S𝛾 = 0.70

59
Bearing Resistance
Partial Factors from R1: 𝛾RV = 1.00
𝑅/𝐴′
= 𝑐′
. 𝑁𝑐. 𝑠𝑐. 𝑖𝑐 + 𝑞′
. 𝑁𝑞. 𝑠𝑞. 𝑖𝑞 + 0.5 . 𝐵′
. 𝛾′
. 𝑁𝛾. 𝑠𝛾. 𝑖𝛾
Total Resistance qult = 2833.65 kPa
Hence, Design Resistance qRd =
𝐪𝐮𝐥𝐭
𝛄𝐑𝐕
= 2833.65 kPa
Rd = 11,334 kN
Vd = 4,200 kN

60
Design Approach DA1-C2 & DA3
Actions and Effects : Design Bearing Pressure = qEd = Vd / Ab = 825.0 kPa
Material properties and Resistance
Design Angle of Shearing Resistance 𝜙d = 30.16˚,
Bearing Capacity Parameters Shape factors
Nq = 18.74, N 𝛾 = 20.62 Sq = 1.50 Sc = 1.58 S𝛾 =0.70
Bearing Resistance
Design Resistance qRd =
𝒒𝒖𝒍𝒕
𝜸𝑹𝑽
= 1271.77 kPa
Rd = 5,087 kN & Vd = 4,200 kN

61
Design Approach 2
Actions and Effects :
Design Bearing Pressure = qEd = Vd / Ab = 1050.0 kPa
Material properties and Resistance
Design Angle of Shearing Resistance 𝜙d = 36.0˚,
Nq = 37.75, N 𝛾 = 53.40 Sq = 1.59 Sc = 1.61 S𝛾 = 0.70
Bearing Resistance
Design Resistance qRd =
𝒒𝒖𝒍𝒕
𝜸𝑹𝑽
= 2024.04 kPa
Rd = 8,097 kN & Vd = 4,200 kN

62
 A square footing resting at a depth of 2.00m on a cohesionless soil with bulk
density γ = 18 kN/m3 is subjected to unfactored dead load (DL) of 80 T and
live load (LL) of 40 T.
 3 Different Problems are considered with variation in Angle of Internal Friction
(φ = 28˚, 30˚ and 36˚)
 Width of Square Footing (B) is obtained for based on current IS Code method
to resist the required DL and LL.
 Using this width (B), the resistance of footing (R) is calculated for different
combinations for LRFD as per EC7.
Resistance (R) is calculated with two considerations:
(I) without considering type of shear failure, using general parameters for all
values for all values of ‘Φ’,
(II) considering type of shear failure based on factored value of ‘Φ’.
62
PROBLEM DEFINITION for PARAMETRIC STUDY

63
63
PROBLEM DEFINITION
Parameters DA1 - C1 DA1 - C2 DA2 DA3
Action, DL 1.35 1.00 1.35 1.00
Action, lL 1.50 1.30 1.50 1.30
Material 1.00 1.25 1.00 1.25
Resistance 1.00 1.00 1.40 1.00

64
64
RESULTS
Parameter
ASD LRFD - EC7
FoS = 2.50
DA1-C1 DA1-C2 /DA3 DA2
Gen
Shear
Local
Shear
Gen
Shear
Local
Shear
Gen
Shear
Local
Shear
DL (T) = 80 108 108 80 80 108 108
LL (T) = 40 60 60 52 52 60 60
Total Load, Q= 120 168 168 132 132 168 168
Φ (Degree) = 28 28 28 23 23 28 28
q,(T/m2
) = 14.51 104.98 36.28 55.45 22.37 104.98 36.28
Width, B (m) = 2.90 2.90 2.90 2.90 2.90 2.90 2.90
Capacity, R = 122.0 882.88 305.11 466.33 188.13 630.63 217.94
R/Q = 1.02 5.26 1.82 3.53 1.43 3.75 1.30

65
65
RESULTS
Parameter
ASD LRFD - EC7
FoS = 2.50
Gen
Shear
Mixed
Shear
Gen
Shear
Local
Shear
Gen
Shear
Mixed
Shear
DL (T) = 80 108 108 80 80 108 108
LL (T) = 40 60 60 52 52 60 60
Total Load, Q= 120 168 168 132 132 168 168
Φ (Degree) = 30 30 30 25 25 30 30
q,(T/m2
) = 25.40 128.08 63.51 67.38 25.88 128.08 63.51
Width, B (m) = 2.20 2.20 2.20 2.20 2.20 2.20 2.20
Capacity, R = 122.9 619.91 307.39 326.12 125.26 442.79 219.56
R/Q = 1.02 3.69 1.83 2.47 0.95 2.64 1.31

66
66
RESULTS
Parameter
ASD LRFD - EC7
FoS = 2.50
Gen
Shear
Gen
Shear
Gen
Shear
Mixed
Shear
Gen
Shear
Gen
Shear
DL (T) = 80 108 108 80 80 108 108
LL (T) = 40 60 60 52 52 60 60
Total Load, Q= 120 168 168 132 132 168 168
Φ (Degree) = 36 36 36 30 30 36 36
q,(T/m2
) = 110.64 276.61 276.61 122.50 61.65 276.61 276.61
Width, B (m) = 1.05 1.05 1.05 1.05 1.05 1.05 1.05
Capacity, R = 122.0 304.96 304.96 135.06 67.97 217.83 217.83
R/Q = 1.02 1.82 1.82 1.02 0.51 1.30 1.30

67
67
SUMMARY
Angle of Int.
Friction (Ø)
Capacity Ratio:
Considering General Shear Failure
Capacity Ratio: Considering
relevant Type of Shear Failure
DA1-C1
DA1-C2
/DA3
DA2 DA1-C1
DA1-C2
/DA3
DA2
28˚ 5.26 3.53 3.75 1.82 1.43 1.30
30˚ 3.69 2.47 2.64 1.83 0.95 1.31
36˚ 1.82 1.02 1.30 1.82 0.51 1.30

69
Excel Sheet for Shallow Foundation Design as per Eurocode - 7

70
Sample Problem Confirming to IS Code Method
Square footing with following data:
Length, L = 2.2 m
breadth, B = 2.2 m
Depth, Df = 2.0 m
Angle of Friction, 𝜙 = 36˚
Effective cohesion, c= 0 kPa
Weight Density, 𝛾 = 18 kN/m3

71
IS Code Method
Failure Type – General Shear Failure
Nc = 50.59 Nq = 37.75 N 𝛾 = 56.31 Sc = 1.30 Sq = 1.20 S𝛾 = 0.80
Depth factors
dc = 1.39 dq = 1.20 d𝛾 = 1.20
Ultimate Bearing Pressure : qult = 2869.30 kPa
Allowable Safe Bearing Capacity : qa = 1147.7 kPa
R = 4,590.8 kN & Q = 3,000 kN

72
Result Summary
Minimum width of square footing is calculated as per IS Code and EC7 guidelines for
general shear failure, local shear failure and mixed shear failure case for square footing
placed at a depth of 2.0m below ground level on cohesionless soil with γ = 18 kN/m3
subjected to an unfactored dead load of 2000 kN and live load of 1000 kN.

73
Design of Pile Foundations: IS 2911 (P-1/Sec2)
For General Shear Failure Criteria: Qsafe = 1/FOS {Qs + Qb)
Qs = Capacity in Skin Friction = Σ (Qsi) for all layers, = 1 to n
Qsi = [Σ( 𝛼. C. L)i + Σ (q’ x Ks. Tanδ . L.)i] x 3.14 x D
q’i = Effective Overburden at the mid depth of the layer.
Ks = Coeff. Of Earth Pressure at Rest, take 1.0
δ = Angle of Wall Friction at the interface of pile and soil, taken as Φ
D = Pile Diameter.
L = Length of Pile for ‘i’ th segment.
C = Cohesion in T/m2.
𝛼 = Mobilization Factor

74
Design of Pile Foundations: IS 2911 (P-1/Sec2)
Qb = Capacity in Base Resistance
= [(9.00 x C) + (q’ x Nq ) + 0.5 D x γ x Nγ ]* 0.785 x D2
q’= Effective Overburden at the base,
Subjected to a max. value at a depth = 20 x pile dia.
Nq = Bearing Capacity factors as per IS-2911 part-1, Section-2,
For Cohesive soil, Nq = 0
FOS = Factor of Safety =2.50.

75
Design of Pile Foundations: Eurocode 7
ULS verifications are carried out with the three possible Design Approaches:
• DA1 – Comb. 1: A1 + M1 + R1
• DA1 – Comb. 2: A2 + M1 + R4 ( For Pile Resistance and Anchors)
A2 + M2 + R4 ( For unfavourable actions e.g. negative skin friction etc)
• DA2 : A1 + M1 + R2
• DA3 : A2 + M2 + R3

76
Partial Resistance Factors for Pile Foundations ( 𝛾R) :

77
L-M-R Combinations for Bored Piles:

KNS_LRFD-GEOTECH_CHANGA_08-09-21-RKS.pdf

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