CIV4249 – Foundation Engineering (Part 1 of 2)
Table of Contents
0. Introduction ...........................................................................................................................................................................................................2
0.1 Unit introduction ............................................................................................................................................................................................2
1. Site Investigation & Insitu Testing .........................................................................................................................................................................3
1.1 Site Investigation Introduction .......................................................................................................................................................................3
1.2 Site Exploration Methods ...............................................................................................................................................................................4
1.2.1 Boreholes ................................................................................................................................................................................................4
1.2.2 Insitu Testing ...........................................................................................................................................................................................5
1.2.3 Sampling..................................................................................................................................................................................................8
1.3 Site Investigation Examples ............................................................................................................................................................................9
2. Foundation Design Parameters ...........................................................................................................................................................................10
2.1 Site Investigation Introduction .....................................................................................................................................................................10
2.2 Parameters required for Designing Foundations ..........................................................................................................................................11
2.3 Methods of obtaining the Design Parameters ..............................................................................................................................................12
2.4 Conceptual Foundations ...............................................................................................................................................................................18
2.5 Conceptual Foundations ...............................................................................................................................................................................19
3. Bearing Capacity of Shallow Foundations ............................................................................................................................................................20
3.1 Introduction to Shallow Foundations ...........................................................................................................................................................20
3.2 Bearing Capacity Theory ...............................................................................................................................................................................22
3.3 Bearing Failure in soils ..................................................................................................................................................................................24
3.4 Bearing Capacity Equations ..........................................................................................................................................................................26
3.5 Stresses below Eccentrically Loaded Footing................................................................................................................................................29
3.6 Shallow foundation design on Layered Soils .................................................................................................................................................30
3.7 Shallow foundations on Rocks ......................................................................................................................................................................33
3.7 Bearing Capacity of Shallow foundations: Special Cases ..............................................................................................................................34
3.7.1 Soil with a Rigid Base at Shallow Depth ................................................................................................................................................34
3.7.2 Stronger Soil Underlain by Weaker Soil (stronger over weak) ..............................................................................................................35
4. Settlement of Shallow Foundations .....................................................................................................................................................................37
4.1 Importance of Settlement Calculations ........................................................................................................................................................37
4.2 Settlement mechanisms in Clay & Sand ........................................................................................................................................................37
4.3 How to calculate Settlement of Footing .......................................................................................................................................................38
5. Shallow Foundation on Reactive Soils .................................................................................................................................................................43
5.1 Introduction to reactive soils and Foundation response ..............................................................................................................................43
5.2 Residential slabs and footings (AS 2870-2011) .............................................................................................................................................44
5.3 Typical foundation solutions .........................................................................................................................................................................46
6. Combined footing and Mat foundation ...............................................................................................................................................................48
6.1 Introduction to Combined footing and a Mat/Raft foundation ....................................................................................................................48
6.2 How to design a Combined footing or a Mat/raft foundation ......................................................................................................................49
6.3 Structural design of Mat foundations ...........................................................................................................................................................50
0. Introduction
0.1 Unit introduction
▪
Unit Learning Outcomes
-
LO1
LO2
LO3
LO4
-
LO5
LO6
▪
Topic of Interest previously covered!
Assess geotechnical investigation carried out for a civil infrastructure development project.
Generate geological models for a development site based on the geotechnical investigation data.
Predict design parameters for materials of interest from the geotechnical investigation results and existing correlations.
Design shallow foundations on complex ground profiles using site specific material properties and satisfying limit states
requirements.
Design pile foundations for complex loads and ground conditions based on limit state and serviceability requirements.
Generate quality reports for geotechnical investigation and design outputs.
It is recommended you revise the following topics:
1. Site investigation (CIV2242-Geomechanics I)
a. Wash boring, Auguring, Coring, borelogs
2. Soil/rock classifications (CIV2242)
a. Unified Soil Classification System (USCS), Rock Mass Rating (RMR) etc.
3. Laboratory and field tests (CIV2242, CIV3247-Geomechanics II)
a. Unconfined compressive strength (UCS), triaxial, direct shear, oedometer etc.
b. Standard Penetration Test (SPT), Cone Penetration Test (CPT) etc.
4. Shear strength & deformation properties (CIV2242, CIV3247)
a. Drained and undrained shear strength properties
b. Drained and undrained deformation properties
c. Consolidation properties of clay
CIV4249: Foundation Engineering
Page 2
2.5 Conceptual Foundations
At this stage, we know:
• How to obtain the ground profile including the thicknesses and compositions of strata
• How to determine relevant foundation design parameters requiring for the ULS and SLS
Now, it’s time to introduce some concept foundation options that include both Shallow foundations (pad footing) &
Deep foundations (piles of various types).
▪
Foundation Design Stages
Conceptual efficiencies for Geotechnical & Structural design
Case 2 = More efficient. If stiff clay, clay
strength ↑ as depth ↑ so its always better to
have longer embedment. Also as strength ↑
w/ depth ∴ modulus ↑ w/ depth. Concrete
volume is also less for deeper pile.
For settlement sensitive structures piles
provide less settlement by transferring load
from surface to deeper stronger strata.
Shallow foundations are settlement
sensitive.
For settlement sensitive structures Raft
slab or pad footing provides large
settlement at center ∴ use Raft supported
by piles.
Timber structures are insensitive to
settlement so we can use cheaper pad
foundations.
Normally consolidated clay will experience
settlement. Whereas dense sand =
compacted sand will have ↓ settlement.
Boring into bedrock or driving to bedrock
are both appropriate & cost-effective.
For piles under tension (uplift) heavier/larger
piles are more desirable.
When subject to lateral loads, must
consider overturning moments
When constructing in sand, driven piles can cause liquefaction. Best to bore piles
CIV4249: Foundation Engineering
Page 19
3.3 Bearing Failure in soils
We have 3 shear failure modes, where the form of failure the ground experiences is based on the ground condition
i.e these Modes describe how the rupture plane is internally developed:
1. General Shear Failure:
-
-
Typical for hard/stiff clay, dense sand etc.
High ultimate bearing capacity of soil/continuous failure surface/sudden failure
Rigid fail lines (active joint) moves in direction of footing movement
As rigid/active soil moves downward surrounding material gives way creating the radial shear joint
Passive joint then causes heaving on surface
(passive joints goes out but then tries to resist the rigids downward movement)
Resistance is along failure plane
*Rupture plane takes circular (log spiral) shape
Gradually load footing and it starts compressing & begins to elastically then plastically deform reaching ultimate capacity
then settles to residual state (residual stress) whereby the soil then maintains this residual capacity (dense materials dilate)
2. Local:
-
Typical for medium dense or firm soils, loose sand
Lower ultimate bearing/slip surface doesn’t extend to surface/higher vertical displacement
Passive joint is absent, rupture in soil is restricted to smaller surface than general shear failure
This happens locally (hence the name)
*Stress/strain is like loose sand (increases to ultimate shear failure)
3. Punching:
-
Typical for loose or soft soils
Lowest ultimate bearing/ soil under footing compresses/ Highest vertical displacement
Liquid form material, soil under footing compresses
No rupture experienced bcas no pressure
Only one failure joint (rigid/active)
Will give lowest failure capacity
Sum resistance from friction and cohesion to get total resistance of ground
CIV4249: Foundation Engineering
Page 24
3.4 Bearing Capacity Equations
▪
How to calculate bearing capacity (Terzaghis bearing capacity equations):
1.
Check material type
o If Clay: (φ’=0) i.e cohesive soil
Check shear strength parameters
o
If Sand: (c’=0) i.e cohesionless soil
Check φ’ = friction angle (take lower bound)
- Founding depth significantly impacts sandy soils
cu = 40 = firm
cu = 100 = stiff
φ' =31= loose
φ'=37=v.dense
2.
Expected failure method:
a) General Shear failure: Typical for hard/stiff clay, dense sand etc.
b) Local failure: Typical for medium dense or firm clays, loose sand
c) Punching failure: Typical for loose or soft soils
Note: Must also consider effect of GW
3.
Choose appropriate equation:
o
If general failure:
o
c’ = cohesion of soil [kPa]
γ = unit weight of soil below Df [kN/m3] ≈ γsat-10
q = γ*Df = use overburden; check if case 1,2 or 3
Nc, Nq, Nγ = bearing capacity factors (table 3.1)
4.
If local or punching failure (must downgrade strength
parameters):
Where,
N’c, N’q, N’γ = modified bearing capacity factors (table 3.2)
Determine safe column loads:
qu = qu(gross) [kPa] = Ultimate gross bearing capacity, as above
qu(net) = Ultimate net bearing capacity = Max pressure soil can support above its current overburden pressure (γD f)
= 𝑞𝑢 − 𝛾 ∗ 𝐷𝑓 (Note: ultimate load carrying capacity = qu(net) *A)
Note: If undrained clay, qu(net) = 1.3*c’*Nc Water table has no effect on qu(net) of undrained clay.
qallow = Allowable bearing capacity [kPa]
𝑞
𝑙𝑜𝑎𝑑 𝑓𝑎𝑐𝑡𝑜𝑟, 𝛹
1.35
= 𝑢 𝑛𝑒𝑡 (where FOS =
=
= 2.7)
𝐹𝑂𝑆
-
𝑔𝑒𝑜 𝑟𝑒𝑑𝑢𝑐𝑡𝑖𝑜𝑛 𝑓𝑎𝑐𝑡𝑜𝑟, 𝛷
0.5
Pc(safe) = qs = Safe bearing pressure = lesser or equal to allowable bearing capacity based on serviceability consideration.
= 𝑞𝑎𝑙𝑙𝑜𝑤 ∗ 𝐹𝑜𝑜𝑡𝑖𝑛𝑔 𝐴𝑟𝑒𝑎 [𝑘𝑁]
𝐹
𝐹
Note: ULS check, 𝛹( ) < 𝛷(𝑞𝑢(𝑛𝑒𝑡) ) to satisfy ULS. Typically 1.35( ) < 0.5(𝑞𝑢(𝑛𝑒𝑡) )
𝐴
CIV4249: Foundation Engineering
𝐴
Page 26
Se = Elastic settlement (immediate or undrained)
To calculate elastic settlement below a flexible footing:
Note: Δσ below footing = α*qo*Is
Where,
Se = Elastic (immediate or undrained) settlement [m]
𝐹
qo = qnet = net applied pressure on foundation = − (𝛾 ∗ 𝐷𝑓 ) [kPa]
𝐴
μs = Poisson’s ratio of soil, for clay = 0.5, for sand ≈ 0.3
Es = average modulus of elasticity of the soil, measured from founding depth @ z=0 to z=5B
B′ = factor = B/2 (at center), or = B (at corner)
α = a factor that depends on the location where settlement is being calculated
= 4 (at center), or = 1 (at corner)
Is = shape factor =
(Is ≈ 0.56 for infinite layer???) (If clay, Is = F1)
If = depth factor (see fig below, apply to total Se if layered soils)
Note: Must apply corrections:
> Embedment correction = is a fnc of Df/B, μs, and L/B, see figure below
> Rigidity correction:
Elastic settlement of multi-layered soils: Calc these for each layer
𝐵
𝐿
o Settlement at centre:
o Settlement at corner: (Try 𝑚′ = 𝑧 & 𝑛′ = 𝑧) z=Df
𝐿
𝐻
′
′
𝐿
𝐻
-𝑚 =
& 𝑛 =
if H = inf, F2 ≈ 0
- 𝑚′ =
& 𝑛′ =
if H = inf, F2 ≈ 0
𝐵
(𝐵/2)
𝐵
- For m’ and n’ find F1 & F2 using tables below
- Calculate Is = shape factor
- Calc Se,layer 1
▪
𝐵
- For m’ and n’ find F1 & F2 using tables below
- Calculate Is = shape factor
- Calc Se,layer 1
Shape (Is) and depth factors (If)
0
0.1
0.2
Values of F1 (
0.3
0.4
) and F 2 (
0.5
)
0.6
0.7
0.8
L/B = 1
L/B = 2
4
F1
I
Depth factor d = H/B
2
L/B = 5
F2
6
L/B = 5
L/B = 10
8
L/B = oo
L/B = 2
L/B = 1
10
L/B = 10
L/B = oo
Influence values for settlement beneath the corner of a uniformly loaded
rectangle on an elastic layer (Depth D) overlying a rigid base
CIV4249: Foundation Engineering
Depth factor (IF), Fox (1948)
Page 40
CIV4249 – Foundation Engineering (Part 2 of 2)
Table of Contents
7. Axial Capacity of Piles.................................................................................................................................................... 2
7.1
Introduction to Deep Foundations.................................................................................................................... 2
7.2
Pile Capacity based on Pile Driving Formulae ................................................................................................... 4
7.2.1 Required design parameters ............................................................................................................................ 6
7.3 Textbook Equations for Estimating Pile Capacity ................................................................................................. 10
7.3.1 Determining Qp .............................................................................................................................................. 10
7.3.2 Determining Qs ............................................................................................................................................... 12
7.4 Downdrag effect on pile design (Negative Skin Friction) ...................................................................................... 15
7.5 Group Piles ............................................................................................................................................................ 16
8. Settlement of Piles ...................................................................................................................................................... 18
8.1
Load-settlement behaviour of a single pile .................................................................................................... 18
8.2
Methods to estimate Settlement of a Single pile ........................................................................................... 19
8.3
Methods to estimate Settlement of a Group pile ........................................................................................... 21
8.4
Consolidation settlement of Group piles (using clay-equivalent raft concept) .............................................. 22
9. Design of Rock Socketed Piles ..................................................................................................................................... 23
9.1 Introduction to Rock Socketed Piles ..................................................................................................................... 23
9.2 Rock Socketed Piles Design Method ..................................................................................................................... 24
9.3 State of practice for the design of socketed piles in rock (Pells-8ANZ) ................................................................ 30
10. AS2159-2009:Piling—Design and installation, highlights + Pile Testing ................................................................... 32
10.1 Introduction to AS2159 ....................................................................................................................................... 32
10.2 Introduction to Pile Testing................................................................................................................................. 35
10.3 Load Testing Methods......................................................................................................................................... 35
10.4 Integrity testing methods.................................................................................................................................... 36
11. Laterally loaded Piles ................................................................................................................................................ 37
11.1 Introduction to laterally loaded piles & their uses ............................................................................................. 37
11.2 Methods of calculating lateral load capacity ...................................................................................................... 38
11.2.1 Brinch Hansen Method (1964) ..................................................................................................................... 40
11.2.2 Broms Method (1965) .................................................................................................................................. 42
11.2.3 Elastic Method ............................................................................................................................................. 44
11.2.4 p-y Method .................................................................................................................................................. 47
11.3 Laterally loaded piles in a group ......................................................................................................................... 49
12. Final Exam ................................................................................................................................................................. 50
12.1 Exam Overview (2019) ........................................................................................................................................ 50
7. Axial Capacity of Piles
7.1 Introduction to Deep Foundations
Piles are structural members that are made of steel, concrete, or timber. They are used to build pile foundations, which are deep and which
cost more than shallow foundations. Despite the cost, the use of piles often is necessary to ensure structural safety. Conditions that require
pile foundations:
•
•
•
•
•
▪
To transfer load to a underlying stronger strata, when upper soil layers ae highly compressible & too weak
To support lateral loads i.e pile foundations resist bending for all structures that are subjected to high wind
or to earthquake forces
To increase the stability i.e when expansive and collapsible soils are present, they swell and shrink as their
moisture content changes, hence pile foundations are extended into stable soil layers beyond this zone
where moisture will change
To carry uplift loads, i.e transmission towers, offshore platforms, and basement mats below the water
table, are subjected to uplifting forces
To avoid scour damage i.e Bridge abutments and piers are usually constructed over pile foundations to
avoid the loss of bearing capacity that a shallow foundation might suffer because of soil erosion
Types of piles
- Major types based on ground response to installation:
o Displacement piles
Pile hammered in & displaces equal volume laterally
> Large displacement (precast concrete piles, timber piles)
> Small displacement (H-piles, screw piles)
> Driven to ground
o
Non-displacement piles
Auger material out & back fill w/ conc & reinf.
> Bored piles
> Cast-in-place piles
- Types of piles also based on load support:
1) Pile put through FBS, MSG and WF then sitting on
Melbourne mudstone & so has much higher capacity
from combined contribution
2) Driving resistance from end-bearing
3) Friction = Driving resistance from interface of pile, base
provides no resistance, like its floating
▪
Design considerations
- Selection of piles is based on:
a) Type of structure and location
b) Ground conditions:
> When hammering piles into v.dense sand may refuse, & at basalts, or at top of EW-HW siltstone, this may impact base of pile
> If thick basalt layer at shallow depth encountered what solution do we need? Is settlement under basalt affordable as we
have softer soils underlying?
c) Durability required
- Types of piles (must consider installation and load support mechanism)
> For friction piles: geotechnical properties govern design as soil is typically weaker than concrete
> For end bearing: rock can often be stronger than conc. so conc. properties govern design
- Soil conditions (granular, cohesive):
> Resistance around shaft and base changes for sands & clays so need to know how to apply eqns.
> Rock has separate design guideline
- Load to be supported (compressive, tensile, lateral)
> Need to know how to design piles under different loads i.e lateral loads are different from tension/comp.
- Group action (block failure, group settlement)
> For big towers may need multiple piles under columns to support loads
- Pile testing (affect geotechnical reduction factor)
> Do more testing on site & improve safety factor as we have more confidence of soil & pile behaviour
CIV4249: Foundation Engineering
Page 2
7.4 Downdrag effect on pile design (Negative Skin Friction)
Negative skin friction is a downward drag force exerted on a pile by the soil surrounding it. This occurs when piles are placed in soft/loose soils
(e.g. in fill, soft clays which settle under self-weight). The impact of negative friction: 1) ↑ axial load on pile & ↑ settlement of pile
Such a force can exist under the following conditions, among others:
1. If a fill of clay soil is placed over a granular soil layer into which a pile is
driven, the fill will gradually consolidate. The consolidation process will exert
a downward drag force on the pile during the period of consolidation.
2. If a fill of granular soil is placed over a soft clay, it will induce the process of
consolidation in the clay layer & ∴ exert a downward drag on the pile.
3. Lowering of the water table will increase the vertical effective stress on the
soil at any depth, which will induce consolidation settlement in clay. If a pile
is located in the clay layer, it will be subjected to a downward drag force.
▪
How to deal w/ downdrag:
Include the maximum downdrag force as axial load and obtain size of the pile
Estimate settlement by including downdrag with axial load
Estimate downdrag force using ESA i.e. 𝜏 = 𝐾 ∗ 𝜎 ′ ∗ tan (𝛿)
Use the full layer thickness in the analysis (conservative). Smaller depth can be found by following Poulos (1997)
Note: Do not account for the effect of downdrag in the ULS analysis. Just do normal analysis.
▪
Design approach for piles with negative friction
- Poulos (2008) introduced a practical design approach to deal w/ negative skin friction problem (not found in textbooks).
> Piles must have adequate geotechnical capacity
> Piles must have adequate structural capacity against axial and negative friction induced loads
> Piles should not exceed tolerable total and differential settlement
- Neutral plane (pile settlement=soil settlement) lies at or below the depth of ground settlement, pile settlement reach a limiting
value and then will not continue to settle as the ground continues to settle.
- This requires that the unfactored capacity of the portion of the pile in the stable zone should equal or exceed the factored load
combinations, including the drag load.
To calculate Negative Skin friction (Qn = Fneg)
o
Negative Skin Friction (Fneg):
𝐹𝑛𝑒𝑔 = 𝐴𝑠 ∗ 𝑓𝑛𝑒𝑔 = 𝐴𝑠 ∗ (𝐾 ′ ∗ 𝜎𝑜′ ∗ tan(𝛿))
Where,
As = surface area of shaft in soft clay layer, if square = 4DL, if circle = πDL [m2]
fneg = The unit negative (downward) skin stress on the pile (Can assume φ’ ≈ 20o for soft clays)
𝐾
K’ = coefficient of horizontal soil stress = ( 𝑠 ) ∗ (1 − sin(𝜃))
𝐾𝑜
σ’o = average effective stress [kPa]
δ = angle of pile/soil friction [o]
Clay Fill over Granular Soil (Figure 11.35a)
The total downward drag force on a pile, Qn, is:
o
Where,
Qn = Negative Skin friction [kN]
p = pile perimeter [m], if square = 4D, if circle = πD
K’ = earth pressure coefficient = (k/ko)*(1 – sin φ’)
γf’ = effective unit weight of fill [kN/m3]. If above water table use moist unit weight
δ = soil pile friction angle = 0.6*φ’ or ≈ 0.5 – 0.7*φ’ (see section 7.2.1)
Hf = Height of fill [m]
Granular Soil Fill over Clay (Figure 11.35b)
In this case negative skin friction only exists from z=0 to z=L1.
o
Where,
L1 = neutral depth [m]
CIV4249: Foundation Engineering
Page 15
9.3 State of practice for the design of socketed piles in rock (Pells-8ANZ)
Following Pells (1999), design method includes 1) Elastic method & 2) Design for side slip (Rowe & Armitage)
Rock Socket Pile Design, Elastic method
1. Calculate ultimate unit socket resistance (fsu):
fsu = Ultimate shaft resistance [kN/m2, kPa]
α = adhesion reduction factor for shaft friction, see graph
β = Reduction factor for discontinuities in rock mass (correction for jointing/discontinuities in rock mass)
(Use graph for Williams & Pells method; all other methods β = 1)
qu = UCS of intact rock (unconfined compressive strength of intact rock sample) [kPa]
(Can use moisture content, w, or convert point load by *10-12 etc to get UCS)
> 𝑈𝐶𝑆 = 104.07−.063∗𝑤 [kPa] for w = moisture content [%]
> 𝑈𝐶𝑆 = 𝐾 ∗ 𝐼𝑠(50) [kPa] for K = 12.6 for mudstone or K = 18 for sandstone/siltstone
2.
3.
4.
Calculate ultimate unit base resistance (fbu):
See section 9.2 for other formulas
qmax = fbu = ultimate unit base resistance [kPa]
σcm = UCS of rock mass = (𝛼𝐸 )0.7 ∗ 𝜎𝑐 [kPa]
σc = UCS of intact rock, see step 1 [kPa]
aE = reduction factor to relate intact rock UCS with rock mass UCS = 0.0231 ∗ 𝑅𝑄𝐷 − 1.32 ≥ 0.15
Calculate downward force due to negative skin friction (Fnegative):
𝐹𝑛𝑒𝑔𝑎𝑡𝑖𝑣𝑒 = 𝐴𝑠 ∗ 𝑓𝑛
Fnegative = downward force due to negative skin friction [kN]
As = surface area of shaft in clay/settling layer, if square = 4DL, if circle = πDL [m2]
fn = unit negative (downward) skin stress on the pile [kPa]:
K’ = earth pressure coefficient = (k/ko)*(1 – sin φ’) (see section 7.2.1)
σo’ = vertical effective stress at middle of settling layer, depth z = γf’*z
δ = soil pile friction angle (see section 7.2.1)
Calculate length of rock socket using Pells (1999):
Assumes length required to support the total limit state load by socket resistance only.
> Total limit state load = 1.35(𝐹𝑎𝑝𝑝𝑙𝑖𝑒𝑑 ) + 1.2(𝐹𝑛𝑒𝑔𝑎𝑡𝑖𝑣𝑒 ) [𝑘𝑁]
> Required length of the socket, L =
Total limit state load
𝐿𝑚𝑎𝑥
𝜋∗𝐷∗𝑓𝑠𝑢
[𝑚] for fsu in [kPa]
𝐿
> Calculate
then superimpose a straight line on fig.8 from Pb/Pt = 100% to point 𝑚𝑎𝑥
𝐷
𝐷
> Intersection of this line with relevant curve Ep/Er gives design solution (Draw new line)
𝐸𝑝
𝐸𝑟
=
𝑌𝑜𝑢𝑛𝑔𝑠 𝑚𝑜𝑑𝑢𝑙𝑢𝑠 𝑜𝑓 𝑝𝑖𝑙𝑒 𝑏𝑎𝑠𝑒
𝑌𝑜𝑢𝑛𝑔𝑠 𝑚𝑜𝑑𝑢𝑙𝑢𝑠 𝑜𝑓 𝑟𝑜𝑐𝑘 𝑚𝑎𝑠𝑠
where Youngs mod of intact rock ≈ Er = 103.511−.078∗𝑤 [MPa]
for w = moisture content [%]
> Read down from new line & intersection, this gives revised L/D
Aim to optimize L/D = 4, or acceptable w/in 4-10
then calculate design length = (revised L/D) * D
> From fig.8 Pb/Pt = x%, this describes load taken by base
CIV4249: Foundation Engineering
Page 30
11.2.2 Broms Method (1965)
Broms Method (earth pressure based, considers shear failure of soil):
- Applicable to both short and long piles in only cohesive or cohesionless soils (no layered soils).
- Maximum moment, shear and deflection at pile head can be determined (Uses design charts to determine capacity & deflection at pile head)
Broms method (1964) Must check ultimate capacity Qu(g) and deflection capacity Qg
o Check if short or long pile:
- Short if L/T < 4 or L/R < 3.5, otherwise treat as long
o
Ultimate capacity for short pile
In Sand:
𝑒
𝑒𝑐𝑐𝑒𝑛𝑡𝑟𝑖𝑐𝑖𝑡𝑦 [𝑚]
1. =
𝐿
In Clay:
𝑒
𝑒𝑐𝑐𝑒𝑛𝑡𝑟𝑖𝑐𝑖𝑡𝑦 [𝑚]
1. =
𝑙𝑒𝑛𝑔𝑡ℎ [𝑚]
𝐿
𝑙𝑒𝑛𝑔𝑡ℎ [𝑚]
2. Length =
𝐷
=
𝐷
𝑑𝑖𝑎𝑚𝑒𝑡𝑒𝑟 [𝑚]
𝐷
3. Ultimate lateral resistance:
𝜑′
> Kp = rankine passive earth pressure coeff. = tan2 (45 + )
2
φ’ = soil friction angle [dego]
> γ = unit weight of soil [kN/m3]
> Then solve
o
𝑄𝑢(𝑔)
𝐾𝑝 ∗𝛾∗𝐷
𝑑𝑖𝑎𝑚𝑒𝑡𝑒𝑟 [𝑚]
𝐿
𝑙𝑒𝑛𝑔𝑡ℎ [𝑚]
2. Length = =
𝑑𝑖𝑎𝑚𝑒𝑡𝑒𝑟 [𝑚]
3. Ultimate lateral resistance:
0.75∗𝑞𝑢
> cu = undrained cohesion ≈
[kPa]
𝐹𝑂𝑆
qu = UCS [kPa] & FOS ≈ 2-3 ≈ 2.5
> Then solve
for Qu(g) = ultimate load resistance [kN]
3
𝑄𝑢(𝑔)
𝑐𝑢 ∗𝐷3
for Qu(g) = ultimate load resistance [kN]
Ultimate capacity for long pile
In Sand:
𝑒
𝑒𝑐𝑐𝑒𝑛𝑡𝑟𝑖𝑐𝑖𝑡𝑦 [𝑚]
1. =
In Clay:
𝑒
𝑒𝑐𝑐𝑒𝑛𝑡𝑟𝑖𝑐𝑖𝑡𝑦 [𝑚]
1. =
2. Yield Moment, My = S*Fy [kNm]
𝐼
𝐼
S = section modulus of the pile section = = 𝑑1𝑝 [m3]
2. Yield Moment, My = S*Fy [kNm]
𝐼
𝐼
S = section modulus of the pile section = = 𝑑1𝑝 [m3]
𝐷
𝑑𝑖𝑎𝑚𝑒𝑡𝑒𝑟 [𝑚]
𝐷
𝑦
𝑏4
𝜋𝑟 4
(2)
𝑏ℎ 3
I: If square = , if circular = , if rectangular =
12
4
12
FY = σy = yield stress of the pile material [kPa]
3. Ultimate lateral resistance:
𝜙′
> Kp = rankine passive earth pressure coeff. = tan2 (45 + )
2
> γ = unit weight of soil [kN/m3]
𝑄𝑢(𝑔)
> Then solve
for Qu(g) = ultimate load resistance [kN]
3
𝐾𝑝 ∗𝛾∗𝐷
CIV4249: Foundation Engineering
𝑑𝑖𝑎𝑚𝑒𝑡𝑒𝑟 [𝑚]
𝑦
𝑏4
𝜋𝑟 4
(2)
𝑏ℎ 3
I: If square = , if circular = , if rectangular =
12
4
12
FY = σy = yield stress of the pile material [kPa]
3. Ultimate lateral resistance:
0.75∗𝑞𝑢
> cu = undrained cohesion ≈
[kPa]
𝐹𝑂𝑆
qu = UCS [kPa] & FOS ≈ 2-3 ≈ 2.5
> γ = unit weight of soil [kN/m3]
> Then solve
𝑄𝑢(𝑔)
𝑐𝑢 ∗𝐷3
for Qu(g) = ultimate load resistance [kN]
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