COURSE FASCILITATOR:
ASSOC. PROF IR. DR. RAMLI NAZIR
PROF. DR. KHAIRUL ANUAR KASSIM
COURSE FASCILITATOR:
By
ASSOC. PROF. Ir. DR. HJ. RAMLI NAZIR UNIVERSITI TEKNOLOGI MALAYSIA
1 FOUNDATION ENG. DESIGN
PRINCIPLES
There is no glory as a Geotechnical Engineer - Terzaghi
2 FOUNDATION ENG. DESIGN
GEOTECHNICAL BRAIN FUNCTION
4 FOUNDATION ENG. DESIGN PRINCIPLES 5 FOUNDATION ENG. DESIGN PRINCIPLES7 FOUNDATION ENG. DESIGN PRINCIPLES
A PROFESSIONAL COMPARISON
8 FOUNDATION ENG. DESIGN PRINCIPLESWhat is Value Engineering in Foundation Design???
Challenge The Norm Thru Innovation
To Excel
VALUE ENGINEERING.
10 FOUNDATION ENG. DESIGN
PRINCIPLES
Stage of Design
• Normally there are 3 stages of design i.e 1. PRE DESIGN STAGE2. CONSTRUCTION STAGE
3. POST DESIGN STAGE
11 FOUNDATION ENG. DESIGN
PRINCIPLES
PRE DESIGN STAGE
• Accurate and reliable SI data is vital.• Type of foundation use for the structure is based from the above. • An overall aspect and anticipation during construction has to be
considered especially practical and economics consideration. • During this stage, loading, foundation arrangement and location,
bearing capacity and other related practice has been identified. • Anticipation of the problem in foundation construction work should be
DESIGN ANALYSES
• Which one to use???• TOTAL STRESS ANALYSIS Or
• EFFECTIVE STRESS ANALYSIS
13 FOUNDATION ENG. DESIGN
PRINCIPLES
TOTAL STRESS ANALYSES
• This type of analysis uses the undrained shear strength of the cohesivesoil and also known as short term analysis.
• The undrained shear strength, cucan be obtained from field such as
vane shear and laboratory such as unconfined compression test. If the undrained shear strength is constant throughout the depth then cu= c
and =0o. The use of unconsolidated undrained triaxial compression
test is also applicable provided that it is saturated plastic soil. • The groundwater does not have an effect in the use of total stress
parameters.
14 FOUNDATION ENG. DESIGN
PRINCIPLES
EFFECTIVE STRESS ANALYSIS
• This type of analysis uses the drained shear strength, c’ and ’ of theplastic soil.
• The drained shear strength could be obtained from triaxial compression test with pore pressure measurement tested on a fully saturated specimen of the plastic soil.
• Also known as long term analysis since the shear-induced pore water pressure (positive or negative) from the loading has dissipated and the hydrostatic pore pressure conditions now prevail in the field. • Thus the location of the water table is significant in considering in the
GENESIS OF FOUNDATION DESIGN
16 FOUNDATION ENG. DESIGN
PRINCIPLES
PRINCIPLE IN GEOTECHNICAL ENGINEERING DESIGN
SI SOIL PROPERTIES GROUND CHARACTERIZATION GROUND BEHAVIOUR ENGINEERING PERFORMANCE • ENGINEERING PROPERTIES • CHEMICAL PROPERTIES • BASIC & INDEX PROPERTIES
• MASS PROPERTIES • TYPICAL & GENERALISED SUBSOIL PROFILE & PROPERTIES OF TYPICAL GEOLOGICAL FORMATIONS, MAN MADE FILL etc.. • ENGINEERING GEOLOGY
SOIL & ROCK MECHANICS • EFFECTIVE STRESS THEORY • SEEPAGE THEORY • STRESS DISTRIBUTION • LATERAL PRESSURE •BEARING CAPACITY • COMPRESSIBILITY INSTRUMENTATION FOR • PORE WATER PRESSURE • EARTH PRESSURE
• DISPLACEMENT(SURFACE & SUBSURFACE • INTERNAL STRESSES CODE OF PRACTICES:-• FOUNDATION BS 8004 •ANCHORS BS8081 •EARTHWORKS BS6031 •REINFORCED FILLS BS8006 •GEOGUIDES INTERPRETATION JUDGEMENT MODELLING PREDICTION DEFORMATION DISPLACEMENT STABILITY 17 FOUNDATION ENG. DESIGN PRINCIPLES
THE IMPORTANCE OF SI
• To study the general suitability of the site for an engineering project. (FEED Program)- FRONTIER EVALUATION ENGINEERING DEVELOPMENT.
• To enable a safe, practical and economic design to be prepared. • To determine the possible difficulties that may be encountered by a
specific construction method.
Cont…
• SI nowdays has become contracting exercise and we tend to forget thatSI is an INVESTIGATION.
• As in many INVESTIGATION it is an itterative process. • For information to be reliable, adhere to the procedure is very
important.
• SI is the most procedure oriented operation within Civil Engineering Discipline.
• This is due to the variability of the soil formation millions of years ago • The properties of oil assessment or test carried out is affected by the
latter.
• Accuracy and correct procedure is of vital important.
19 FOUNDATION ENG. DESIGN
PRINCIPLES
The Facts Why SI is needed
• This is a part of geotechnical processes. • Lack of geotechnical processes will lead toa:-• Failures where many case histories are available.
• Significant delay and increase in construction costs when the design has to be revised or ammended.
• Generally the elimination of the SI will not safe the cost of the project thus it only comprises from only 0.1% to 5% of the project cost. • In fact most frequent claims in civil engineering contracts are on the
basis of inadequate SI or obstructions resulting in extra costs which could not reasonably have been forseen by an experience contractor.
20 FOUNDATION ENG. DESIGN
22 FOUNDATION ENG. DESIGN
PRINCIPLES
YOU HAVE TO PAY FOR THE S.I
WHETHER YOU LIKE IT OR NOT!!
23 FOUNDATION ENG. DESIGN
PRINCIPLES
Method of Site Investigation
• JKR PROBE/MACKINTOSH PROBE
• HAND AUGERING (HA)
• MOTORISED HAND BORING (MHB)
• DEEP BORING (DB)
• TRIAL PITS AND PLATE BEARING TEST
• DEEP SOUNDING (DS)
• INSITU VANE SHEAR TEST (IVST)
• STANDARD PENETRATION TEST (SPT)
• PRESSUREMETER TEST
25 FOUNDATION ENG. DESIGN PRINCIPLES 26 FOUNDATION ENG. DESIGN PRINCIPLES
HAND AUGERING
28 FOUNDATION ENG. DESIGN PRINCIPLES 29 FOUNDATION ENG. DESIGN PRINCIPLESBEARING PLATE
31 FOUNDATION ENG. DESIGN PRINCIPLES 32 FOUNDATION ENG. DESIGN PRINCIPLES34 FOUNDATION ENG. DESIGN PRINCIPLES 35 FOUNDATION ENG. DESIGN PRINCIPLES
STANDARD PENETRATION TEST (SPT)
37 FOUNDATION ENG. DESIGN PRINCIPLES 38 FOUNDATION ENG. DESIGN PRINCIPLES40 FOUNDATION ENG. DESIGN PRINCIPLES 41 FOUNDATION ENG. DESIGN PRINCIPLES
STANDARD PENETRATION TEST (SPT) • This a dynamic field test usually carried out in boreholes.
• Test consists of driving a standard split barrel sampler 50.8mm in diameter.
• The SPT is read from a 65kg drop hammer fall at a vertical height of 75cm.
• The sampler is driven to a total of 45cm into the soil and the number of blows recorded for the last 30cm of penetration (SPT, N-value)
43 FOUNDATION ENG. DESIGN
PRINCIPLES
Numbers of BH, POSITION and Depth
44 FOUNDATION ENG. DESIGN
46 FOUNDATION ENG. DESIGN PRINCIPLES 47 FOUNDATION ENG. DESIGN PRINCIPLES
STANDARD PENETRATION TEST
VALUE FOR DESIGN
• Developed in 1927 and currently the most popular method and economical means to obtain subsurface information.
• Currently 85% - 90% of usage in conventional foundation design.
• Test consist of :-• Driving the split barrel sample at a distance of 460mm into the soil at the bottom of boring. • Counting the number of blows to drive sample at last two 150mm distances to obtain N value • Using 63.5kg driving mass falling free from a height of 760mm.
if:-• When full test depth cannot be obtained, boring log will show a ratio as 70/100 or 50/100 indicating that 70 or 50 blows resulted in a penetration of 100mm.
• The blow count is directly related to the driving energy:-• Substituting Both Equations : m
= v= 2 2gh = Wh For standard test:‐ E = 63.5 x 9.81 x 0.762 = 474.5 ~ 475 kJ
W= weight of mass or hammer H = height of fall
49 FOUNDATION ENG. DESIGN
PRINCIPLES
• Kovac and Salomone ( 1982) found that the actual energy impact to the sampler range about 30% to 80% while Riggs (1983) obtained energy input from 70% to 100% • The discrepancies arises
from:-• Equipment from different manufacturers • Driving hammer configuration • Usage of liner inside the barrel • Overburden pressure • Length of drill rod
• Therefore SPT can be standardised to some energy ratio Ersuch
that:-Er= (Actual hammer energy to sampler (Ea)/ Input Energy (E)) x 100
50 FOUNDATION ENG. DESIGN
PRINCIPLES
• Energy input of 70% is normally use since observation is close to the actual energy ratio (Er)
• Therefore the standard blow count N’70is measure from N as
follows:
N’70= CNx N x x x x
Where i = adjustment factor from table
N’70= Adjusted N
52 FOUNDATION ENG. DESIGN PRINCIPLES 1 2 r 1 r 2 2 r 1 1 r xN E E 2 N xN E xN E
• Note that larger Erdecrease the blow count nearly linearly
i.e Er45gives N=20
Er90gives N = 10
With Er70gives N = 13
• Energy ratio x blow count should be constant thus :-Say Er1= 70 thus gives N2= (70/Er2)xN1
Say N2for Er45= 20 = Er2
We obtain N1= 13
If we convert N70to N60 than N2 = N60 = (70/60)x13 = 15
• Using the equation we can readily convert any energy ratio to any other base. 53 FOUNDATION ENG. DESIGN PRINCIPLES
SPT CORRELATIONS
20 N 5 . 4 70 • It can be used in correlation for unit weight relative density, Dr,
angle of internal friction angle , undrained compressive strength, qu,
bearing capacity and stress-strain modulus. • Angle of internal
friction:-Base from Japanese Railway Standard: • Relative Density
Base from Meyerhof(1957) : where p’ois in kPa
• For OCR > 1 Skempton suggest the following adjustment has been made:-o 2 r 70 ' p 288 . 0 32 D ' N 70 ' p BC A ' N
Where A range between 15 to 54 B range between 0.306 to 0.204 And
For COCR=1 it relates to normally consolidated clay
Thus Meyerhof
estimate:-• A correlation for N versus quin general form
of:-qu= kN
Where k tend to be site dependant.
However k = 12 has been used i.e for N’70= 10, qu= 120kPa
OCR OCR o onc
p
p
C
'
'
r D o 15 o 28 55 FOUNDATION ENG. DESIGN PRINCIPLESDESIGN N-values
56 FOUNDATION ENG. DESIGN PRINCIPLESRelationship between Angle of Internal Friction and N-Value
(Sandy Soil) 58 FOUNDATION ENG. DESIGN PRINCIPLES Hammer Type SPT c (t/m2) = 2/3 N
N-SPT = Total No. of Blows for spoon sampler to penetrate at a depth of 30cm
SPT (Standard Penetration Test)
59 FOUNDATION ENG. DESIGN
PRINCIPLES
Relationship between Cohesion and N-Value (Cohesive soil)
61 FOUNDATION ENG. DESIGN PRINCIPLES 62 FOUNDATION ENG. DESIGN PRINCIPLES
PRESSUREMETER TEST
ROCK CORING
• To determine the soundness of rock.• Sound rock : Rock which ring when struck with a pick or bar. Does not integrate after exposure to air or water, breaks with a sharp, fresh fracture, in which cracks are unweathered and less than 3mm wide and generally not closer than 1m apart. Core recovery is normally 85%.
• Medium rock : Characteristic as for sound rock but the cracks maybe 6mm wide and slightly weathered, generally no closer than 60cm. Core recovery is 50% or more.
• Intermediate rock : Give dull sound when hit by pick or bar. Does not integrate after exposure to air or water. Broken pieces may show weathered faces. Fractures up to 25mm wide and space no closer than 30cm. Core recovery generally is 35% or greater.
• Soft rock : Any rock which flakes on exposure to air or water. Give a very dull sound when struck with pick or bar. Core recovery generally is less than 35% or greater but SPT more than 50.
64 FOUNDATION ENG. DESIGN PRINCIPLES 65 FOUNDATION ENG. DESIGN PRINCIPLES
Strength of Rock Materials
Term Uniaxial Compressive Strength (MN/m2)
Very Weak < 1.25
Depending on moisture , anisotrophy and test procedure Weak 1.25 – 5.0 Moderately Weak 5.0 – 12.5 Moderately Strong 12.5 – 50.0 Strong 50 - 100 Very Strong 100 - 200
SOIL SAMPLING TECHNIQUE
• 2 TYPES OF SAMPLE:-• Undisturbed : To determine properties such as strength parameters, consolidation, permeability and parameters which need to observed as per site condition.
• Disturbed : Do determine physical properties such as grain size, colour, texture, compaction properties, remoulded properties and for testing etc.
67 FOUNDATION ENG. DESIGN
PRINCIPLES
FIELD IDENTIFICATION AND DESCRIPTION OF SOIL
• Soil descriptions are made from washed and disturbed samplesrecovered from the boreholes.
• The soil name is based on particle size distribution and plasticity, which can be readily estimated and measured at the laboratory.
68 FOUNDATION ENG. DESIGN
PRINCIPLES
• According to BS 5930, soil samples are described with each element of the descriptions having a fixed position within the overall
description:-• a) Consistency (cohesive) or RD (non cohesive) • b) Fabric and Fissuring, if distinguishable • c) Colour
• d) Subsidiary constituent
• e) Angularity or grading of principal soil type (for coarse grained soil) • f) Principal soil type (in capital letter)
• g) More detailed comments on constituents or fabric. EG.
Very Stiff (a) Dark Grey (c) CLAY (f)
Dense (a) Brown (c) Fine to Coarse (e) Angular (e) GRAVEL (f)
• When soils are desribed at field, it is important to learn how to distinguish between clay and non cohesive soils on the basis of estimated engineering behaviour. (10% of clay can impart an essentially cohesive behaviour. Eg.
• A soil containing 50% of silt, 30% of clay and 20% of sand is described as sandy silty CLAY because the soil behaves more like a clay.
• Clayey SAND – not cohesive, but contains clay
• Very clayey SAND or Very sandy CLAY – borderline
• Sandy CLAY – cohesive, but sand may be the major constituents by weight.
70 FOUNDATION ENG. DESIGN
PRINCIPLES
CONSTRUCTION STAGE
• Engineers should allow or apt with changes during construction of foundation at site.
• Alternative design need to be in hand whenever there are changes during this stage.
• At this stage a critical, fast and accurate decision need to be done as the delay in making decision will hold or retarding the process of construction.
• This is a stage where foundation engineers are really tested in their knowledge integrity.
• This is also a stage where reliability of SI data is known.
71 FOUNDATION ENG. DESIGN
PRINCIPLES
POST DESIGN STAGE
• To validate the design, load test need to be carried out. The designer may choose to have them conducted either before or after the bids are taken.
• The first alternative permits development or revision of design and specifications to fit the actual conditions.
• The second saves expenses on mobilisation but may lead to delay if the results is unsatisfactorily.
PILE LOAD TEST AND INTERPRETATION
73 FOUNDATION ENG. DESIGN PRINCIPLES 74 FOUNDATION ENG. DESIGN PRINCIPLES76 FOUNDATION ENG. DESIGN PRINCIPLES 77 FOUNDATION ENG. DESIGN PRINCIPLES
79 FOUNDATION ENG. DESIGN PRINCIPLES 80 FOUNDATION ENG. DESIGN PRINCIPLES
82 FOUNDATION ENG. DESIGN PRINCIPLES 83 FOUNDATION ENG. DESIGN PRINCIPLES
LOAD TEST
To ensure the pile workability before and after construction. It is also as a method to determine settlement and ensuring that it does not exceed allowable limit.
Failure of load test according to JKR specification:-1. Residual settlement at working load exceed 6.5mm 2. Total settlement at working load exceed 12.5mm
3. Total settlement exceed 38mm or 10% of pile diameter or width whichever is lower at twice working load.
• The time lapse is sufficient for excess pore water pressure to dissipates. • Pile in cohesive soils should be tested after sufficient lapse for excess
pore water pressure to dissipates.
• This time lapse is commonly in the order of 30 to 90 days giving also some additional strength gain from thixotropic effects.
85 FOUNDATION ENG. DESIGN PRINCIPLES 86 FOUNDATION ENG. DESIGN PRINCIPLES
NEW FAILURE INTERPRETATION
i) The total residual settlement after removal of the test load at working load exceeds ((diameter of pile or diagonal width for non-circular pile / 120) + 4) mm or 12.50 mm whichever is the lower value.
ii) The total settlement under twice the Working Load exceeds 38.0 mm, or 10% of pile diameter / width whichever is the lower value.
2DL sett le m ent DL 6.5mm 12.5mm 38mm 88 FOUNDATION ENG. DESIGN PRINCIPLES
Failure Load Definition
1. NAVFAC Method
2. Van Weele
3. Chin Fung Kee Method
4. DeBeer Method
5. Mazurkiewicz Method
89 FOUNDATION ENG. DESIGN PRINCIPLESNAVFAC Method
91 FOUNDATION ENG. DESIGN
PRINCIPLES
Van Weele Method
92 FOUNDATION ENG. DESIGN
PRINCIPLES
• From point O to ‘a’ the capacity is based on the skin resistance plus any small point contribution. • From point ‘a’ to ‘b’ the load capacity is the sum of the limiting skin resistance plus the point
capacity.
• From point ‘b’ the curves becomes vertical as the ultimate point capacity is reached. Often the vertical asymptote is anticipated and the test terminated before a vertical curve branch is established.
250k
Chin Fung Kee Method
94 FOUNDATION ENG. DESIGN PRINCIPLES 95 FOUNDATION ENG. DESIGN PRINCIPLESDe Beer Method
Load (Log Scale)
Set
tlement (Log Scale)
The load settlement curve is plotted in log-log plot and the point of intersection of the two straight lines thus obtained is the failure load. 97 FOUNDATION ENG. DESIGN PRINCIPLES
Mazurkiewicz Method
98 FOUNDATION ENG. DESIGN PRINCIPLES Load Set tlement45o He assumed that the load
settlement curve is parabolic after an initial straight portion . The ultimate load can be obtained by geometric construction. After the initial straight portion, draw sets of equal settlement lines to intersect the load settlement curve. Draw vertical line loads from this intersection to intersect
the load axis. Draw 45o line to
intersect the next load line. The intersection fall in a line which
STARTING POINT OF FOUNDATION DESIGN
• Following steps are the minimum requirement for designing afoundation.
1. Locate the site and the position of the load
2. Physical inspect the site for any geological or other evidence that may indicate potential design problems
3. Establish the field exploration program for design parameters 4. Determine necessary design parameters base on integration of test
data, scientific principles and engineering judgement.
5. Design the foundation using the latter and it should be economical and be able to be built by the available construction personnel.
100 FOUNDATION ENG. DESIGN
PRINCIPLES
GENERAL REQUIREMENT
TWO MOST IMPORTANT QUESTION FOR DESIGNER!!!
• WHAT LOADS ARE TO BE SUPPORTED.
• HOW FAR MAY THE FOUNDATION SETTLE IN RESPONSE TO
THESE LOAD.
101 FOUNDATION ENG. DESIGN
PRINCIPLES
• Generally the proper design requires the following:-1. Determine the building purpose, probable service life
loading, type of framing, soil profile, construction methods and construction cost.
2. Determine the client owner and client needs.
3. Making the design, but ensuring that it does not successively degrade the environment and provide a margin of safety that produces a tolerable risk level to all parties, the public, the owner and the engineer.
ADDITIONAL CONSIDERATION IN FOUNDATION
DESIGN
• Adequate depth
• Depth of foundation to be below seasonal change • Considering problematic soil
• Compressive strength consideration • Protection of foundation against natural causes • Sustainable to changes
• Buildable or limitation. • Apt to local environment standard.
103 FOUNDATION ENG. DESIGN
PRINCIPLES
CHOICE OF FOUNDATION TYPE
• Based from Neoh C.A, the choice of the foundation designs areconsidered from: 1. Loads per column
2. Bearing type either end or skin 3. Bearing layer
4. Type of Intermediate layer 5. Location of water level.
104 FOUNDATION ENG. DESIGN
PRINCIPLES
Assess Foundation Base
Assess Ground Conditions and Type of Structures Are pile necessary Choose Shallow Foundation Types Technical Considerations for Different Pile Types:-1. Ground Condition 2. Loading Condition 3. Environmental Considerations 4. Site and Plant Considerations 5. Safety
List all technically feasible pile types and rank them in order of suitability
Assess construction programme for each suitable pile type and rank them based on program consideration
Make overall ranking of each pile type based on technical, cost and programme considerations
Submit individual and overall rankings of each pile
NO YES
PROCEDURE FOR THE CHOICE OF FOUNDATION TYPE FOR A SITE
106 FOUNDATION ENG. DESIGN
PRINCIPLES
Myths in Piling
• Myth
• Dynamic Formulae such as Hiley’s Formula Tells us the Capacity of the Pile
The Truth
• Pile Capacity can only be verified by using: • (i) Maintained (Static) Load Tests • (ii)Pile Dynamic Analyser (PDA) Tests
107 FOUNDATION ENG. DESIGN
PRINCIPLES
Continue
• Myth:
• Pile Achieves Capacity When It is Set. • Truth:
• Pile May Only “Set” on Intermediate Hard Layer BUT May Still Not Achieve Required Capacity within Allowable Settlement.
Myth:
• Pile settlement at 2 times working load must be less than certain magnitude (e.g. 38mm)
• Truth:
Continue
• Myth
• Load test can opt not to be done since the pile has all set. • Truth
• Load test need to be done since it is part of Geotechnical Design process i.e to verify. Pile set does not mean that it has reach its allowable capacity at designated settlement.
109 FOUNDATION ENG. DESIGN PRINCIPLES 110 FOUNDATION ENG. DESIGN PRINCIPLES
112 FOUNDATION ENG. DESIGN PRINCIPLES 113 FOUNDATION ENG. DESIGN PRINCIPLES
THE END
115 FOUNDATION ENG. DESIGN
APPLICATION OF EUROCODE IN GEOTECHNICAL DESIGN
ASSOC. PROF. Ir. DR. HJ. RAMLI NAZIR DEPT. OF GEOTECHNIC AND TRANSPORTATION,
UNIVERSITI TEKNOLOGI MALAYSIA
INSPIRING CREATIVE AND INNOVATIVEMINDS
Lecture 2
UNDERSTANDING THE DESIGN USING EUROCODE (EN-7 (MALAYSIAN ANNEXE))
INSPIRING CREATIVE AND INNOVATIVEMINDS
INTRODUCTION
• The Eurocode system consists of :1. EN1990 Eurocode 0 Basis of Design
2. EN1991 Eurocode 1 Actions on Structure 3. EN1992 Eurocode 2 Design of Concrete Structures 4. EN1993 Eurocode 3 Design of Steel Structures 5. EN1994 Eurocode 4 Design of Composite Steel and
Concrete Structures 6. EN1995 Eurocode 5 Design of Timber Structures. 7. EN1996 Eurocode 6 Design of Masonry Structures 8. EN1997 Eurocode 7 Geotechnical Design
OBJECTIVES OF THE EUROCODES
• As a mean to prove compliance of building and civil engineering works with the essentialrequirements of mechanical resistance and stability and safety in case of fire. • A basis for specifying contracts for construction works and related engineering services. • A framework for drawing up harmonised technical specs for construction products. • Improve the functioning of a single market for products and engineering services by
removing obstacles arising from different nationality codified practices for the assessment of structural liabilities.
• Improve the competitiveness of the European construction industry and its professionals and industries, in countries outside the European Union.
Eurocode Design Method
• All the Eurocodes are all based on a common design method • The common design method is presented in EN 1990
• A common loading code for all the Eurocodes is presented in EN1991- Actions • The Eurocodes share a common terminology and symbols
• The common design method for the verification of safety and serviceability involves – The limit state design method
– Partial factors
– Characteristic actions and material parameters or resistances – Reliability based
Q: Why do we need a change?
• Eurocode 7 draws geotechnical design into a framework common to other aspects of civil and structural engineering.
• In the past, differences in design approach have arisen due to the properties of soil and rock being fundamentally different and more difficult to predict than other engineering materials.
• In order to overcome difficulties in prediction and uncertainty of material behaviour, designers have often adopted large factors of safety under working loads to ensure serviceability.
• However, to avoid problems, designers need to grasp fundamental geotechnical principles, including overall stability, hydraulic uplift and piping.
Contd…
• Eurocode 7 may be seen by some as an unnecessary complication, it introduces theconcepts of limit state design to geotechnical calculations.
• This will be second nature to most structural engineers who will not find any difficulty with the concepts.
• The currently accepted methods of analysis of geotechnical problems remain largely unchanged.
• The real advantage in its application lies in a common framework for design, including overall stability, and uplift.
• The Eurocodes adopt, for all civil and building engineering materials and structures, a common design philosophy based on the use of separate limit states and partial factors rather than global factor of safety.
• The intended are to ensure safe structures, so they will be use both by the designers and the checkers of the design.
COMPARISON BETWEEN CONVENTIONAL DESIGN AND EUROCODES
• Advantages :
Conventional Design Eurocode
Using Global FOS and simple
applications Using PFOS and harmonic design Accustomed to use Type of load has different levels of uncertainty
Uniform Level of Safety Risk Assessment
COMPARISON BETWEEN CONVENTIONAL DESIGN AND EUROCODES
• Disadvantages :
Conventional Design Eurocode
Inadequate amount of variability More Complex Stress is not a good measure of
resistance Old Habits
FOS is subjective Requires availability of statistical data No risk assessment Resistance Factor varies
Whereabout in Eurocodes ?
The suite of primary structural Eurocodes
Numbers Name Subject
EN1990 Basis of structural design
EN1991 Eurocode 1 Action on structures
EN1992 Eurocode 2 Design of concrete stuctures
EN1993 Eurocode 3 Design of steel structures
EN1994 Eurocode 4 Design of composite steel and concrete structures
EN1995 Eurocode 5 Design of timber structures
EN1996 Eurocode 6 Design of masonry structures
EN1990
EN1990
• EN 1990 describes the Principles and requirements for safety, serviceability and durability of structures.
• It is based on the limit state concept used in conjunction with a partial factor method. • For the design of new structures, EN 1990 is intended to be used, for direct application,
together with Eurocodes EN 1991 to 1999.
• EN 1990 also gives guidelines for the aspects of structural reliability relating to safety, serviceability and durability:
– for design cases not covered by EN 1991 to EN 1999 (other actions, structures not treated, other materials) ;
– to serve as a reference document for other CEN TCs concerning structural matters.
EN1990
• EN 1990 is intended for use by :
– committees drafting standards for structural design and related product, testing and execution standards ;
– clients (e.g. for the formulation of their specific requirements on reliability levels and durability) ;
– designers and constructors ; – relevant authorities.
• EN 1990 may be used, when relevant, as a guidance document for the design of structures outside the scope of the Eurocodes EN 1991 to EN 1999, for :
– assessing other actions and their combinations ; – modelling material and structural behaviour ; – assessing numerical values of the reliability format
EN1990
• This standard gives alternative procedures, values and recommendations for classes with notes indicating where national choices may have to be made.
• Therefore the National Standard implementing EN 1990 should have a National annex containing all Nationally Determined Parameters to be used for the design of buildings and civil engineering works to be constructed in the relevant country.
• National choice is allowed in EN 1990 through : • – A1.1(1)
• – A1.2.1(1) • – A1.2.2 (Table A1.1) • – A1.3.1(1) (Tables A1.2(A) to (C)) • – A1.3.1(5)
• – A1.3.2 (Table A1.3) • – A1.4.2(2)
ASSUMPTIONS
• The general assumptions of EN 1990 are :• the choice of the structural system and the design of the structure is made by appropriately qualified and experienced personnel;
• execution is carried out by personnel having the appropriate skill and experience; • adequate supervision and quality control is provided during execution of the work, i.e. in
design offices, factories, plants, and on site;
• the construction materials and products are used as specified in EN 1990 or in EN 1991 to EN 1999 or in the relevant execution standards, or reference material or product specifications;
• the structure will be adequately maintained;
• the structure will be used in accordance with the design assumptions.
TERMS USED
• ‘Principles’ are mandatory (‘Normative’) requirements; ‘Principle’ clauses in the Code are identified by a ‘P’ after the clause number and contain the word ‘shall’. • All other clauses are ‘Application Rules’ that indicate the manner in which the design
may be shown to comply with the Principles.
• Application Rules are ‘Informative’ (i.e. not mandatory and for Information only) and use words such as ‘should’ and ‘may’.
EN1997
What is the structure of the new code?
• Eurocode 7 consists of two Parts: Part 1 (EN 1997-1) – Geotechnical design – General rulesand Part 2 (EN 1997-2) - Ground investigation and testing.
• It is important to appreciate that EN 1997-1 is not a detailed geotechnical design manual but is intended to provide a framework for design and for checking that a design will perform satisfactorily; that is, that the structure will not reach a ‘limiting condition’ in prescribed ‘design situations’.
• The Code therefore provides, in outline, all the general requirements for conducting and checking design.
• It provides only limited assistance or information on how to perform design calculations and further detail may be required from other texts, such as standard soil mechanics books and industry publications.
EN1997
• Part 2 covers Ground Investigation and Testing.
• The application of the code in the Malaysia requires reference to the Malaysia National Annexes which provide the partial factors prescribed for use in the Malaysia. • The Malaysia National Annex for Part 1 will be available in 2012 and the National Annex
for Part 2 is expected to be published after that since it is still in progress. • A series of geotechnical execution standards covering geotechnical processes such as
piling works and grouting also exist; these are primarily of interest to construction, but are also of general interest to designers.
EN1997
• It describes the general ‘Principles’ and ‘Application Rules’ for geotechnical design, primarily to ensure ‘safety’ (adequate strength and stability), ‘serviceability’ (acceptable movement and deformation) and ‘durability’ of supported structures, that is of buildings and civil engineering works , founded on soil or rock.
• ‘Principles’ are mandatory (‘Normative’) requirements; ‘Principle’ clauses in the Code are identified by a ‘P’ after the clause number and contain the word ‘shall’. • All other clauses are ‘Application Rules’ that indicate the manner in which the design
may be shown to comply with the Principles.
• Application Rules are ‘Informative’ (i.e. not mandatory and for information only) and use words such as ‘should’ and ‘may’.
Content of EN1997-1
• BS EN 1997-1 contains the following Sections:• Section 1 General
• Section 2 Basis of geotechnical design • Section 3 Geotechnical data
• Section 4 Supervision of construction, monitoring and maintenance • Section 5 Fill, dewatering, ground improvement and reinforcement • Section 6 Spread foundations
• Section 7 Pile foundations
• Section 8 Anchorages (Still not Apply in Malaysia) • Section 9 Retaining structures
• Section 10 Hydraulic failure • Section 11 Site stability • Section 12 Embankments.
Annexes
• The Annex is ‘informative’ which means that the partial factors listed must be used; however, the values of these factors are a matter for national determination and the values shown in the Annex are thus only ‘recommended’
• Annex A
– Annex A is used with Sections 6 to 12, as it gives the relevant partial and correlation factors, and their recommended values, for ultimate limit state design.
– Annex A is normative , which means that it is an integral part of the standard and the factors in it must be used, although their values are informative and may therefore be modified in the National Annex.
• Annex B
– Annex B gives some background information on the three alternative Design Approaches permitted by EN 1990 and given in EN 1997-1
• Annex C - H
– Annexes C to G provide examples of internationally recognised calculation methods for the design of foundations or retaining structures;
– Annexes C to J are informative , which means that in principle, they may be superseded in the National Annex
SUMMARY OF ANNEXES
Traditional Design Philosophies
• FOS on the materials is applied in the choice of the stresses used in the design of the piles and pile caps as structural members.
• When pile considered single, the working load shall not exceed the allowable bearing capacity. The ultimate value shall be obtain from load tests whenever practicable. In general a value of 2 to 3 is normally used.
• Settlement or differential settlement at working load shall not be greater than can be tolerated by the structure.
• When settlement is not critical a smaller FOS can be employed. • The basis of design will be use allowable value and check the settlement.
Limit state design
• An understanding of limit state design can be obtained by contrasting it with “working state design”
• Working state design : Analyse the expected, working state, then apply margin of safety. • Limit state design : Analyse the unexpected states at which the structure has reach an
unacceptable limit.
• Make sure the limit states are unrealistic or at least unlikely.
DESIGN PHILOSOPHY IN EN1997-1
• EN 1997-1 is a ‘limit state design’ code; this means that a design that complies with itwill prevent the occurrence of a limit state • A limit state could, for example, be:
– an unsafe situation – damage to the structure – economic loss.
• While there are, in theory, many limit states that can be envisaged, it has been found convenient to identify two fundamentally different types of limit state, each of them having its own design requirements:
– ultimate limit states (ULS); – serviceability limit states (SLS).
Ultimate Limit Stress
• ULSs are defined as states associated with collapse or with other similar forms ofstructural failure (e.g. failure of the foundation due to insufficient bearing resistance). • In geotechnical design, ULSs include:
– failure by excessive deformation, – loss of stability of the structure or any part of it.
• Hence, a state in which part of a structure becomes unsafe because of foundation settlement or other ground movements should be regarded as a ULS even if the ground itself has not reached the limit of its strength.
Contd….
• Ultimate limit states of full ‘collapse’ or ‘failure’ of geotechnical structures are fortunately quite rare.
• However, an ultimate state may develop in the supported structure because of large displacement of a foundation, which has itself not ‘failed’.
• This means, for example, that a foundation may be stable, after initially settling (it hasn’t ‘exceeded a ULS’ or ‘failed’), but part of the supported structure may have failed (for example, a beam has lost its bearing and collapsed owing to substantial deformation in the structure).
What is the general approach to design?
• The principal emphasis of Eurocode 7 is in the definition and application of partialfactors of safety.
• Factors are applied to characteristic actions, nominal dimensions and characteristic material properties.
• These are considered through calculation with a view to ensuring that the design effects are less than or equal to the design resistances.
• Where relevant, the code requires a total of five different ultimate states to be considered.
Contd…
• EQU: the loss of equilibrium of the structure or the ground, considered as a rigid body, in which the strengths of structural materials and the ground are insignificant in providing resistance;
• STR: internal failure or excessive deformation of the structure or structural elements, including footings, piles, basement walls, etc, in which the strength of structural materials is significant in providing resistance;
• GEO: failure or excessive deformation of the ground, in which the strength of soil or rock is significant in providing resistance (e.g. overall stability, bearing resistance of spread foundations or pile foundations);
• UPL: loss of equilibrium of the structure or the ground due to uplift by water pressure (buoyancy) or other vertical actions;
• HYD: hydraulic heave, internal erosion and piping in the ground caused by hydraulic gradients.
Contd…
• An exception to the application of partial factors is made in relation to water pressure. • It is recognized that the application of partial factors to water pressure can, in some
circumstances, lead to unrealistically high water pressure. In this case, it is suggested that a suitable margin of safety be applied to characteristic water levels. • Three basic design approaches are permitted in the assessment of ultimate limit states
and are applied according to local practice.
What limit states need to be considered?
• For most simple geotechnical design situations, the GEOlimit state will be critical to thesizing of foundations and structural members.
• The sections of the code covering specific design issues, such as pile foundations and spread footings etc., give advice on the limit states that need to be considered. • Where groundwater is present in excavations or cuttings, the UPLand HYDlimit states
need to be considered.
• The STRlimit state is less well defined, but is nevertheless very important in some design situations.
• The STRcase might become critical where imposed loading causes deformation of some part of the structure or deformation of the ground imposes deformation on a structural member.
Which frequently used ?
• For most of the design problems likely to be encountered the STR and GEOultimate limit states are the ones that will apply, as they cover the routine design of shallow and pile foundations and other ‘common’ geotechnical structures.
• The EQU ULS is intended to cater for the rare occasion when, for example, a rigid retaining wall, bearing on a rigid rock foundation, could rotate about one edge of its base.
• The UPL and HYD ULSs, while more common than EQU, are generally beyond the ‘routine’
Unrealistic possibility
Serviceability Limit States
• SLSs are defined as states that correspond to conditions beyond which specified servicerequirements for a structure or structural member are no longer met (e.g. settlement that is excessive for the purposes of the structure).
• It is a non technical statement • (i)P The limit states that concern
:-- The functioning of the structures or structural members under normal use; - The comfort of people;
- The appearance of the construction works - Shall be classified as serviceability limit states (SLS)
Inconvenience, disappointments and more manageable costs. Should be rare, but it might be uneconomic to eliminate them completely.
Who should carry out geotechnical design?
• Part 1 provides a useful, although optional, definition of categories of geotechnicalstructures.
• Geotechnical Category 1 (GC1) includes relatively straightforward structures in which routine methods, including prescriptive methods, may be used.
• While the code makes no attempt to define levels of competency, experienced civil and structural engineers should be capable of preparing the geotechnical design basis for Category 1 structures.
• A designer should be capable of judging whether a design situation is not more complex than allowed within the Geotechnical Category.
Contd…
• Structures that involve excavation below the water table, but otherwise conventionalstructures without unusual risk, are defined as Geotechnical Category 2 (CG2). • Such structures normally require some form of geotechnical characterisation based on
field or laboratory testing.
• The terms ‘geotechnical engineer’, ‘geotechnical specialist’ and ‘geotechnical advisor’ are defined.
• It was suggested that design work on CG2 structures should be carried out by an experienced civil or structural engineer.
Contd…
• Geotechnical Category 3 (GC3) covers situations that are considered unusual or are associated with high risk.
• GC3 projects will typically involve advanced field or laboratory testing and numerical analysis.
• The Association of Geotechnical Specialists advocates the role of Geotechnical Advisors in establishing the design strategy of large projects, and this would seem to be appropriate to GC3 structures.
En1990 fundamental equation for ULSs
Fundamental limit states requirement
Design values of action
6.3.1 Design values of actions
(1) The design value Fd of an action F can be expressed in general terms as: Fd=FFrep
with
Frep=FK
Where F = Partial Factor of Safety for the action which takes account the possibility of unfavourable deviations of the action values from the representatives value. Frep= The relevant representative values for the action
FK = The characteristic values of the action is either 1.0 or
Contd…
Contd..
Contd..
Design values of geometrical data
Basis of geotechnical design
• Refer details to EN7: Geotechnical Design Part 1 : General Rules Section 2 page 19 onwards.
2.1 Design requirement 2.2 Design situations 2.3 Durability
2.4 Geotechnical Design by Calculation 2.5 Design by prescriptive measures 2.6 Load tests and tests on experimental models 2.7 Observational method
DESIGN APPROACH
• Generally EN1997 provides 3 Design Approach for the application of partial factor of Safety.
• The Design Approach is know as DA-1/1, DA-1/2 (Design Approach 1), DA – 2 (Design Approach 2) and DA-3(Design Approach 3)
• MALAYSIA PRACTICE USE ONLY DESIGN APPROACH 1 FOR STR and EQU IN THE DESIGN.
What combinations of partial factors to use?
• Combination 1 involves the consideration of factored actions and unfactored materialproperties and resistances.
• Combination 2 considers unfactored actions, except unfavourable variable actions, and factored material properties.
• Difficulties arise with the application of numerical methods, such as finite element, in the assessment of ultimate state.
• In this case, the factoring of soil strength or stiffness can lead to the generation of inappropriate mechanisms in the analysis.
Contd…
• Uncertainty can also be experienced in assessing slope stability, where it can be difficult to separate favourable and unfavourable actions, and in the design of ground anchors where the design and execution codes provide conflicting advice.
• Serviceability states are usually assessed by adopting unfactored actions and material properties.
DESIGN APPROACH 1 (M’SIA PRACTICE)
• National choice is permitted in the use of a Design Approach for the STR and GEO limit states (see MS EN 1997-1:2012, 2.4.7.3.4.1(1)P).
• As indicated in Table NA1, only Design Approach 1 is to be used in Malaysia. • Table NA1 of this national annex lists the clauses in MS EN 1997-1:2012 where national
choice may be exercised in respect of factor values for design in Malaysia. • Where choice applies, Table NA1 indicates where values are given, or states a value to
be used, or describes the procedure for specifying the factor. • The values given in the Tables in Annex A of this national annex replace the
recommended values in Annex A of MS EN 1997-1:2012.
ONLY FOR DESIGN APPROACH 1 - STR AND GEO Clause 2.4.7.3.4.2
• Other than pile and anchor use
Combination 1 : A1 + M1 + R1 Combination 2 : A2 + M2 + R1
• For Axially loaded Pile and Anchor
Combination 1 : A1 + M1 + R1 Combination 2 : A2 + (M1 or M2) + R4
where M2 is for calculating any
unfavourable actions such as negative skin or transverse loading.
INSPIRING CREATIVE AND INNOVATIVEMINDS
DESIGN APPROACH 1 (M’SIA PRACTICE)
SUMMARY FOR FACTOR OF SAFETY
SUMMARY OF GEOTECHNICAL DESIGN BY
CALCULATION
CHARACTERISTIC MATERIALS PROPERTIES
DIVIDED BY MVALUES
DESIGN MATERIALS PROPERTIES
VERIFY Ed≤ R
dDESIGN RESISTANCE, Rd
DESIGN EFFECT ANALYSIS, Ed
REPRESENTATIVE ACTION, Fk
MULTIPLIED BY FVALUES
DESIGN ACTION, Fd
Geotechnical Design Analysis
THE DESIGN IS ALL ABOUT
Actions:(loads, forces etc.) and Material Properties (c, tan , etc)
DESIGN VALUES OF ACTIONS
CHARACTERISTIC ACTIONS, Fk DESIGN EFFECT OF ACTION, Ed REPRESENTATIVE ACTION, Frep DESIGN ACTION, Fd
Correlation Factor, rep Partial Factor of Safety, rep
GEOTECHNICAL ENGINEERING STUDENT
CIVIL ENGINEERS
FINALLY - HOW TO LOOK SMART FOR ENGINEERS
DESIGN OF SHALLOW FOUNDATION
ASSOC. PROF. Ir. DR. RAMLI NAZIR TEL : 013 7927925
OFF: 07 5531722
INSPIRING CREATIVE AND INNOVATIVEMINDS
Lecture 3
DESIGN OF SHALLOW FOUNDATION
INSPIRING CREATIVE AND INNOVATIVEMINDS
• Basic Consideration in designing the shallow footings
are:-1. Significance and use
2. Settlement limitations
3. Total Settlement
4. Differential settlement
5. Bearing Capacity
Stability Problem
Bearing Capacity Failure
• How do we estimate the maximum bearing pressure that
the soil can withstand before failure occurs?
DESIGN REQUIREMENT
• The design must meet two principle requirement of the Limit State:-1. Capacity is sufficient to support loads
2. Avoiding excess settlement which might lead t a loss of function.
• This limit state is known as Ultimate Limit State and Serviceability Limit State.
• Both states must always be considered in the design.
• This philosophies is the basis of Eurocode 7.
• The concept related to shallow foundation design can be shown in the figure below.
Bearing Capacity and Limit Analysis
Types/Modes of Failure
• general shear failure
• local shear failure
• punching shear failure
Mode (a)
• As the pressure increase towards failure value, qf, a state of plastic
equilibrium is reached initially in the soil around the edges of footing.
• As the soil is not perfectly level , the soil movement will accompany with tilting and heaving to one side of the footing.
• This mode is typical for low compressibility soil where the peak value is significant.
• Ultimately the state of plastic equilibrium is fully developed throughout the soil above the failure surface.
• This type of failure is called a general shear failure.
Mode (b)
• There is a significant compression of the soil under the footing and only partial development of the state of plastic equilibrium.
• The failure surfaces does not reach the ground surface and only slight heaving occurs.
• Tilting of foundation will less been expected.
• The ultimate bearing capacity is not well defined.
• This mode is associated with high compressibility and is called Local Shear Failure.
Mode (c)
• Relatively to high compression of soil under the footing.
• This will accompanied by shearing in a vertical direction around the footing.
• No heaving occurs on the ground surface away from the edges of footing and no tilting occurs.
• Large settlement is the main characteristic of this mode.
• The bearing capacity is not well defined.
• In general, he mode of failure depend on the compressibility of the soil and the depth of foundation related to the breadth.
General Guidelines
• Footings in clays -
general shear
• Footings in Dense sands
( > 67%)-
general shear
• Footings in Loose to Medium dense
(30%< < 67%) -
Local Shear
• Footings in Very Loose Sand ( < 30%)-
D
rpunching shear
r
D
r
D
• The bearing capacity problem can be considered in terms of plastic theory.
• It can be assumed that the stress-strain behaviour of the soil can be represented by the rigid-perfectly plastic idealization.
S
hear S
tress
Y’
• Both yielding and shear failure occur at the same state of stress.
• Unrestricted plastic flow takes place at this stress level.
• A soil mass is said to be in a state of plastic equilibrium if the shear stress at every point within the mass
• The plastic collapse will occur after plastic equilibrium has reach in part of the soil mass.
• This will result in the formation of unstable mechanism ( The par of the soil mass slip)
• The applied load including body forces is called collapse load.
• Determination of the collapse load is achieved using the limit theorem of plasticity known as limit analysis to calculate LOWER and UPPER BOUND to the true collapse load.
LOWER BOUND THEOREM
• If the state of stress can be found which at no point exceeds the failure criterion for the soil and is in equilibrium with the external load system, than there will be no collapse.
• Therefore the external load system constitute a lower bound to the true collapse since a more efficient stress distribution may exit, which would be in equilibrium with higher external loads.
UPPER BOUND THEOREM
• If a kinematically admissible mechanism( the motion of a sliding mass must remain continuous and be compatible with any boundary restriction) of plastic collapse is postulated and if, in an increment of displacement, the work done by the system of external loads is equal to the dissipation of energy by the internal stresses, then collapse will occurs.
• The external load system constitute an upper bound to the true collapse loads since more efficient mechanism may exist resulting in collapse under lower external loads.
BEARING CAPACITY IN
UNDRAINED MATERIALS
UPPER BOUND APPROACH MECHANISM UB-1
• For undrained condition the failure mechanism within the soil mass should be a slip lines which are either a straight line or a circular arcs or both. • For simplification a straight line is used
to identify the three sliding block of a soil under vertical loading. • The load will push downwards and the
blocks will have to move to form a mechanism and therefore be kinematically admissible. • As a result a slip line shown OA, OB,
OC,AB and BC which are the results of energy dissipation along this line.
• The energy line is shown as in the velocity diagram known a hodograph. • It is use to determine the velocities along
the slip line
• Starting with the known vertical displacement (v) of a footing, the point f is known. Block A must move 45ohorizontal
to the stationary soil. The vertical component of this motion must equal to v so the soil and footing will remain contact. • Two construction line may be added to the
hodograph to represent the two limiting conditions.
• The crossing line will meet at point a and form velocity vOA. Similar to Block B where
it moves horizontally with respect to O and at 45owith respect to A. the process
continuously move which is therefore a kinematically admissible.
• The energy dissipated (Ei) due to shearing at relative velocity vialong a
slip line of Length Liis given by :
• Total energy dissipated in the soil can then be found by summingEifor all slip lines.
Slip Line Stress,f Length, Li Relative velocity, vi Energy Dissipated, Ei OA cu 2 2 cuBv OB cu B 2v 2cuBv OC cu 2 2 cuBv
• The work done Wi by a pressure qi acting over an area per unit length Bi moving at velocity vi is given by
:-• For qf, the pressure acting downward while for Block C as the motion
move upwards, the surcharge pressure will tend to move against gravity. This is negative work. Therefore the work done for surcharge (q) will be:
• Summing W for all component:
• Therefore, for mechanism UB-1, for undrained materials the bearing capacity qfis :
=
UPPER BOUND APPROACH,
MECHANISM UB-2
• Another mechanism approach is by replacing Block B with a number of smaller wedges. These wedges describe a circular arc of Radius, R between the rigid block A and block C which is known as shear fan. • Block A and C will move in the same
direction and b the same magnitude. • The velocity around the edge of the
circular arc will be constant as its rotates around point X.
• Since Liis circular length then Li= R • Thus giving :
• The total amount of energy disipated is by summing all amount of energy across all wedges.
• If the wedges angle is small, this summation becomes an integral over a full internal angle of the zone ().
,
Slip Line Stress,f Length, Li Relative velocity, vi Energy Dissipated, E i
OA c
u
2
2 cuBv
Fan Zone (/2) cu R = vfan= 2 cuBv
OC c
u
2 2
cuBv
Total Energy,Ei=
• Applying the same equation as previous for UB-1 it yields :
The results in UB-2 is lower than UB-1, so UB-2 present the true collapse load by upper bound theorem.
LOWER BOUND APPROACH –
STRESS STATE LB-1
• In undrained condition the yield criterion are satisfied without considering mode of deformation thus f= cu. • For equilibrium purposes, 1in zone 2
must be equal to 3in zone 1. • The major principal stress at any point in
zone 1 is :
• The minor principal stress in zone 2 is smilarly :
• If the soil is undrained with shear strength cu, it is in the state of plastic yielding and the diameter of each circle is 2cu. • At the point where the circle meet :
Lower Bound Approach, Stress State LB-2
• A more realistic stress state forming a fan zone which gradually rotate the major principle stress from vertical beneath the footing to horizontal outside.
• The change in direction of major principle stress across a frictional discontinuity depend on the frictional strength along the discontinuity , d.
• In crossing the discontinuity, the major principle stress will rotate by an amount
∆ And the radius of the Mohr circles are cu;
∆ → ; →
=
• For a fan zone of frictional discontinuities substended to an angle , the equation can be integrated as follow across the fan angle fan
:-The principal stress rotation required in the fan is : , giving
:- ∴
This value is higher than for LB-1 so LB-2 represent a better estimate of the true collapse load by the lower bound theorem.
BEARING CAPACITY FACTOR
(Undrained Materials)
• General Equation : (refer pg. 157, App. D, EN7-1)
• For the case of footing surrounded by surcharge pressure q, Nc= 5.14 where Nc is bearing capacity factor for strip footing under undrained conditions (f= cu) • Skempton (1951) provided figure by the side
with included value(solid line) suggested by Salgado et.al. (2004) given that
:-. (Eqn 8.18) Where d : footing depth and B : footing width. For general rectangular footing dimension B x L, Eurocode 7 recommends that shape factor :
Footing in Layered Undrained Soil
• Values of Ncobtained previously may be used for stratified deposits, provided the value of cu for a particular stratum is not greater than the average value for all strata within the significant depth by more than 50% of the average value.
• Merifield et al. (1999) presented upper and lower bound values for Ncfor strip footing resting on a two cohesive layer as a function of thickness H on upper layer of strength cu1 overlying deep deposit materials with strength cu2.
• Proposed design value Ncas suggested in general terms from Figure (a) is valid if the undrained shear strngth of the upper layer is used in the latter equation. (cu= cu1)
• The resulting shape factor for square footing B/L=1 is given as in Figure (b).
Footing Associated With Slopes
• For foundation constructed close to the slope, inevitably the bearing capacity will reduced. • Georgiaids (2010), proposed charts for Nc for
strip footing set back from the crest of the slope with angle by a multiple of the foundation width.
• These are based on upper bound analyses in which an optimal failure mechanism was found giving the lowest upper bound. • Thus it is important to include both local and
global failure mechanism. • The value of Ncreduces with the slope
increment.
• If the foundation is set far enough back from the crest of the slope (l>2B), then the slope will have no effect on the bearing capacity and consider as a level ground (Nc= 2 + )
Variation of c
uwith Depth
• Davies and Booker(1973) conducted upperand lower bound plasticity analyses for soil with linear variation of undrained shear strength with depth z below founding plane
:-Where cu0is the undrained shear strength at z = 0 and C is the gradient of the cu-z relationship. The general expression is the given as:
BEARING CAPACITY IN DRAINED
MATERIALS
Upper Bound Theorem
• The slip surface within the kinematically admissible failure mechanism is either straight lines or spiral log curves or both.
• Normally for drained materials it is a cohesionless soil where c’ = 0 and will exhibit some amount of dilatancy ( ’). • In special case where ( ’), the direction of
movement will be perpendicular to resultant force, Rs.
• The condition is known as normality principle and it represent an associative flow rules.
• Figure (a) shows a failure mechanism in a weightless cohesionless soil (=c’=0) with a friction angle ’ which is similar to UB-2 but log spiral replacing circular fan. • To determine the geometry of the
mechanism, the equation describe the log spiral must be first found. • Thus
:-
Which may be integrated from roat =0 to r at .