Lina - W10 Lecture-Analysis of Raft and Basement
Lina - W10 Lecture-Analysis of Raft and Basement
Lina - W10 Lecture-Analysis of Raft and Basement
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Trapezoidal
Combined
Footing
Strap Footing
Isolated spread
foundation of column
carrying large loads
where space is tight.
The size of the
foundation will
uniformly distribute Uses a strap beam to connect an eccentrically loaded column
pressure on the soil. foundation to the foundation of an interior column.
Maybe used in place of trapezoidal or rectangular combined
footings when allowable soil bearing capacity is high and the
distances between the columns are large.
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Beam
Column
(a) Flat plat – the raft is of uniform thickness
(b) Flat plate thickened under columns
(c) Beams and slab – the beam run both ways and the columns are
located at the intersection of the beams © 2011 Cengage Learning Engineering. All
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(d) Flat plates with pedestal Comparison of isolated foundation and mat foundation
(e) Slab with basement walls as a part of the raft – the wall act as (B = width, Df = depth)
stiffeners for the mat.
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6 - 15 6 - 16
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Slide 18
Compensated Raft Foundation
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below
Consolidation
settlement under a mat
foundation
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Coefficient of subgrade
reaction, k
If a foundation width B is
subjected to a load per unit
area of q, it will undergo a
settlement, .
The coefficient of subgrade
𝑞
reaction: 𝑘 =
Δ
For foundation on sandy
soil, For long beams, Vesic (1961)
𝐵+0.3 2 proposed an equation for estimating
𝑘= 𝑘0.3 (kN/m3) subgrade reaction,
2𝐵
For foundations on clays 12 𝐸𝑠 𝐵4 𝐸𝑠
0.3 𝑘 ′ = 𝐵𝑘 = 0.65
𝑘 = 𝑘0.3 (kN/m3) 𝐸𝐹 𝐼𝐹 1 − 𝜇2 𝑠
𝐵
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Example 8.8
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Example 8.8
(cont.)
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6 - 46
WEEK 10
INTRODUCTION
Piled rafts optimize the advantages of pile
Piled Rafts: foundations and raft foundations. They have
emerged as a way to provide economical
foundation systems for very tall buildings.
An Overview
Piled rafts are relatively new and are
By:
Ir. Dr Norazzlina M.Sa’don, PEng, MIEM
becoming increasingly popular. Some
Geotechnical Engineering Research Group prominent tall buildings built on piled rafts are:
(GERG) UNIMAS • Burj Khalifa tower (Dubai)
• Petronas twin towers (Kuala Lumpur, Malaysia)
• Jeddah tower (Saudi Arabia)
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45
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Load–Settlement Plots of Unpiled and Piled Load–Settlement Plots of Unpiled and Piled
Rafts Under Different Design Conditions Rafts Under Different Design Conditions
Figure 14.2 shows the load-settlement plots for three The curves in Figure 14.2 are discussed
curves (curves 1, 2, and 3), along with the case
where the load is applied on a raft only (curve 0). next to illustrate the advantages of piled
rafts. For all four options, the design load is
Pd and the settlement has to be limited to
Sa.
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Load–Settlement Plots of Unpiled and Piled Load–Settlement Plots of Unpiled and Piled
Rafts Under Different Design Conditions Rafts Under Different Design Conditions
Curve 0: Raft only Curve 1: Piles designed with
conventional safety factor
When the design load is plus raft
carried only by the raft,
the settlement exceeds The piles are designed to carry
most of the load with a
the allowable value, but conventional safety factor (e.g.,
there is no problem with 2.0), allowing for a small fraction
of the design load to be carried
the bearing capacity. by the raft.
The raft may behave
elastically in carrying the The settlement is within the limit.
At the design load, the load-
design load Pd. settlement plot is approximately
linear. The bearing capacity is
high and the system can carry a
larger load.
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Load–Settlement Plots of Unpiled and Piled Load–Settlement Plots of Unpiled and Piled
Rafts Under Different Design Conditions Rafts Under Different Design Conditions
Curve 2: Piles designed with Curve 3: Piles designed to full
lower safety factor plus raft capacity plus raft
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Poulos–Davis–Randolph Poulos–Davis–Randolph
Simplified Design Method Simplified Design Method
Three-way interaction Since settlements play a more important role
takes place among than the bearing capacity in the design of
the soil, pile, and the piled rafts, we will focus more on the stiffness
raft, which makes (K) defined as
rigorous analysis of a
problem very
complex.
The subscripts p and r refer to pile and raft,
The design requires respectively. The approximate methods do
more sophisticated not take the differential settlements into
modelling such as a account.
finite element analysis.
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Poulos–Davis–Randolph Poulos–Davis–Randolph
Simplified Design Method Simplified Design Method
The Poulos–Davis-Randolph Figure 14.4 shows a simplified tri-linear The relative proportion carried by
(PDR) method suggests that load-settlement plot OABC, the raft (X) is defined as:
the vertical bearing represented by three straight line
capacity of the piled raft segments.
may be taken as the lesser
of the following: Along OA, both piles and the raft
a. Sum of the ultimate remain elastic, with the piles reaching
capacities of the raft their full capacity at A, where the total
and all piles applied load on the piled raft is P1.
b. Ultimate capacity of the
block containing the The slope of the line OA is the stiffness Where
piles and the raft, plus of the piled raft Kpr. At any point on
the portion of the raft OA, the total load (Pt) is shared by the
outside the perimeter of raft (Pr) and the piles (Pp).
the piles © 2011 Cengage Learning Engineering. All
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Poulos–Davis–Randolph Poulos–Davis–Randolph
Simplified Design Method Simplified Design Method
If the ultimate load carrying capacity of the piles alone is Pup, the The piled raft stiffness Kpr is defined as
load P1 (Figure 14.4) can be determined as
Based on elastic analysis, Clancy and Randolph (1996) define X Where Kp = stiffness of the pile group alone,
as Kr = stiffness of the raft alone, and
rp = pile-raft interaction factor.
Both Kr and Kp can be estimated from elastic theories.
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Determination of rp
Determination of rp
This figure shows a simple piled-raft model where a single pile is
shown along with an equivalent raft or cap. The pile cap area is To determine the piled raft stiffness Kpr, it is
defined as the raft area divided by the number of piles. necessary to determine the pile raft interaction
o rc = radius of pile cap (based on factor rp. This can be determined as
the raft area divided by the
number of piles)
o r0 = radius of pile
o L = pile length
o Es0 = Young’s modulus of the soil
at the pile head
o Esl = Young’s modulus of the soil
at the pile tip Where
o Esb = Young’s modulus of the
bearing stratum below the pile
tip
o Esav = average Young’s modulus © 2011 Cengage Learning Engineering. All
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of the soil along the pile shaft
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Case Study:
Determination of rp Burj Khalifa Tower in Dubai
The radius of influence of the pile rm is defined as 60
50
40
where
30
y-coordinate (m)
20
-10
-20
and s = Poisson’s ratio of the soil
-30
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-40
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20 30 Reserved.
40 50 60
x-coordinate (m)
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Facts: Facts:
❑ The Burj Khalifa Tower is presently the tallest building in the ❑ The site investigation was carried out in four, with a total of 33
world. boreholes extending to 60–90 m, with one extending to 140 m.
❑ It consists of a 160–story and 828 m high tower with a 4–6 story
❑ Hundreds of standard penetration tests covering all boreholes
podium around the base.
and 60 pressure meter tests limited to five boreholes were
❑ The podium also acts as a base, anchoring the tower to the
ground. conducted, along with geophysical tests for measuring wave
❑ The triple–lobed footprint of the building resembles a desert velocities and determining the soil profile.
flower from the region, and maximizes the views of the Persian ❑ The soil profile consisted of medium dense to very loose silty
Gulf and provides good natural lighting. sand overlying weak calcareous sandstone interbedded with
❑ The entire construction used 330,000 m3 of concrete and very weakly cemented sand, with the water table lying at 2.5
39,000 metric tons of rebar.
m below the ground level.
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Facts: Facts:
❑ The foundation of the tower consists of a piled raft, where a 3.7 ❑ High density low permeability concrete was used in the
m thick raft supported by 194 high performance reinforced foundation, with a cathodic protection system under the raft
concrete bored piles of 1500 mm diameter and approximately to minimize corrosion. In piled raft systems, piles are used
47.5 m length, with a minimum center-to-center spacing of 2.5 mainly to limit the settlements.
times the pile diameter socketed into weak rock.
❑ Static pile load tests were carried out on approximately 1% of
❑ Each bored pile had a capacity of 3000 metric tons. The raft the piles, which were loaded to 1.5 times the working load 4
and piles made of self-compacting concrete with water- weeks after construction. Dynamic pile load tests were carried
cement ratio less than 0.30, placed in a continuous pour using out on approximately 5% of the piles.
a tremie.
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