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The Isl amic university - Gaza
Faculty of Engineer ing
Civil Engineer ing Department
CHAPTER(5)
Inst ructor : Dr. Jehad Hamad
Allowable Bearing Capacity& Settlement
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oIt was mentioned in Chapter 3 that, in many cases, the allowable
settlement of a shallow foundation may control the allowable
bearing capacity. The allowable settlement itself may be controlled
by local building codes. Thus, the allowable bearing capacity will be
the smallerof the following two conditions:
Introduction
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oThe settlement is divided into two categorizes:
Elast ic (Immediate set t lement).
Consolidat ion set t lement.
oIn some calculations of settlement it is required to find the increase
in stress at any depth of soil mass, so we will discuss the calculation
of increase in stress.
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Vertical stress increase insoil mass
to concent rated load:Due-1
X, Y and Z are the coordinates of point
under consideration.
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to circularly loaded area load:Due-2
q o: Load per unit area on circle.
B: Diameter of circle.
r: Distance from center of circle to point
under consideration.
z: Depth of point under consideration.
Go to table ( 5.1 )
find o Ds / q by determining the terms:
r/(B/2)
z/(B/2)
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q o : Load per unit area on rectangle.
I: influence factor.
The point should be under corner of rectangle, if not we have to
divide the rectangle to sub rectangles for which the point is a corner
for each part .
find I, by determining the terms:
see table 5.2
rectangular loaded area:Below-3
Iq o=
Z
Bm=
Z
Ln=
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:loaded areaAverage vert ical increase in st ress due to rectangular-4
When we have a foundation on a layer of soil has depth from z=0 to
z=H, the increase of stress decrease as the depth of soil increase, so
to calculate the average stress increase in such layer use the following
equation:( )
1)1(
2)2(
12
)1(1)2(2
1/2
HHTake;
HHTake;
=
=
=
aHa
aHa
HaHa
oHHavg
II
II
HH
IHIHq
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Go to figure 5.7 to find a I by determining the terms:
H
Bm =2
Ln =2
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1-Elast ic s ett lement ov er saturated clay: ( )s
oavge
E
BqAAS 21=
Go to figure 5.14 to find A1 by determining the terms (H/B and L/B).
Go to figure 5.14 to find A2 by determining the term (Df/B).
Es = !. cu
See Table 5.7 to get a typical value of != f (OCR , PI)
Sett lement calculat ions:
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2- Calculat ion of elast ic set t lement b ased o n elast ic i ty theory:
see table 5.8,9,10
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In 1999, Mayne and Poulos presented an improved formula for calculating the
elastic settlement of foundations. The formula takes into account the rigidity of
the foundation, the depth of embedment of the foundation, the increase in the
modulus of elasticity of the soil with depth, and the location of rigid layers at a
limited depth. To use Mayne and Pouloss equation, one needs to determine the
equivalent diameter Beof a rectangular foundation, or
oImp roved Equ at ion for Elast ic Set t lement :
Where:
B = width of foundation
L = length of foundat ion
For circular foundat ions Be = B
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o Improved equation for
calculating elast ic sett lement:
general parameters
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3-Elast ic set t lement of sand y s oi l us ing strain inf luence factor :
( )=
=
=2
0
'
21
zz
z s
ze z
E
IqqCCS
qq
qC
=
'15.01C1 Correction factor for depth of emb edment :
+=
1.0
yearsinTimelog2.012CC2 Creep correct ion factor :
fD=
qStress at the level of foundat ion inclu ding external loads and soi l w eight.
q Effect ive vert ical overburd en pressure. In the absence of water table
.
Es: Modulus of elast ic i ty of so i l below the found at ion w hich is var iable.
Why Es i s v ari ou s?
Due to n onhom ogenu ity o f so il th e value o f Es is varying , w e can est im ate the
value o f Es from field tes ts as Standard Penetrat ion Number (N) or Cone
Penetrat ion Resistance( )cq
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( ) ( )
NIb
mKNftt
ftIbftUS
q
q
ftUSNmKNN
E
c
cs
=
4484.4
27854.952
220002
22
1
//1
//tons1
footingstripFor5.3
footingsquareorcircularFor5.2
tons/8or/766
zI : Strain inf lu ence factor, it is given as shown b elow:
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Z Iz
0 0.1
Z1=0.5B 0.5Z2=2B 0
For square or circular foundation
Z Iz
0 0.2
Z1=B 0.5Z2=4B 0
For foundation with L/B 10
For L/B between 1 and 10, we have to do interpolation for each depth.
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The procedure for calculat ing elast ic sett lement using Eq. (5.49) is given here
(Figure 5.22):
Step 1. Plot the foundation and the variation of Iz with depth to scale (Figure 5.22a).
Step 2. Using the correlation from standard penetration resistance (N60) or cone
penetration resistance (qc), plot the actual variation of Es with depth (Figure 5.22b).
Step 3. Approximate the actual variation of Es into a number of layers of soil having
a constante Es, such as Es(1), Es(2), . . . , Es(i), . . . Es(n) (Figure 5.22b).
Step 4. Divide the soil layer from Z = 0 to Z = Z2 into a number of layers by drawing
horizontal lines. The number of layers will depend on the break in continuity in the Iz and Es
diagrams.
Step 5. Prepare a table (such as Table 5.11) to obtain
Step 6. Calculate C1 and C2.
Step 7. Calculate Se from Eq. (5.49).
=
=
2
0
zz
z s
z zEI
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Procedure for calculation of Se using t he st rain inf luence factor
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Meyerhof (1956) proposed a correlation for the net bearing pressure for
foundations with the standard penetration resistance, N60. The net pressure has
been defined as
Sett lement of Foundat ion on Sand Based on Standard
Penet rat ion Resistance Meyerhof s Method
According to Meyerhof s theory, forAccording to Meyerhof s theory, for 2525 mm (mm (11 in) of est imated maximum set t lement,in) of est imated maximum set t lement,
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Since the time that Meyerhof proposed his original correlations, researchers have
observed that its results are rather conservative. Later, Meyerhof (1965) suggested
that the net allowable bearing pressure should be increased by about 50%. Bowles
(1977) proposed that the modified form of the bearing equations be expressed as
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Burland and Burbidge (1985) proposed a method of calculating the elastic settlement
of sandy soil using the field standard penetration number, N60 (See Chapter 2.)
The method can be summarized as follows:
1. Variation of Standard Penetration Number with Depth
Obtain the field penetration numbers N60 with depth at the location of the
foundation. The following adjustments of N60 may be necessary, depending on the
field conditions:
For gravel or sandy gravel,
oBurland and Burbidges Method
For fine sand or silty sand below the
15>groundwater table and N60
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2. Determination of Depth of Stress Influence (Z):
In determining the depth of stress influence, the following three cases may arise:
Case I. If N60 [or N60 (a) ] is approximately constant with depth, calculate from
Case II. If N60 [or N60 (a) ] is increasing with depth, use Eq. (5.65) to calculate Z
Case III. If N60 [or N60 (a) ] is decreasing with depth Z = 2B, or to the bottom of soft
soil layer measured from the bottom of the foundation (whichever is smaller).
3. Calculat ion of Elast ic Sett lement Se :
The elastic settlement of the foundation Se, can be calculated from
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As mentioned before, consolidation settlement occurs over time in saturated clayeysoils subjected to an increased load caused by construction of the foundation.
(See Figure 5.29.) On the basis of the one-dimensional consolidation settlement
equations given in Chapter 1, we write
o Primary Consolidation Settlement Relationships
(for normally consolidated clays)
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The consolidation settlement calculation presented in the preceding section is
based on Eqs. (1.61), (1.63), and (1.65). These equations, as shown in Chapter 1,
are in turn based on one-dimensional laboratory consolidation tests. The
underlying assumption is that the increase in pore water pressure u,
immediately after application of the load equals the increase in stress!, at any
depth. In this case,
oThree-Dimensional Effect on Primary
Consolidation Settlement
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Circular foundat ion on a clay layer
Kcir = set t lement rat io for circular
foundations.
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Sett lement rat ios for circular (Kcir)
And Cont inuous foundat ions
(Kstr)
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At the end of primary consolidation (i.e., after the complete dissipation of excess pore
water pressure) some settlement is observed that is due to the plastic adjustment of soil
fabrics. This stage of consolidation is called secondary consolidat ion.
o Settlement Due to Secondary Consolidation
Variation of ewith log t under a given
load increment , and definit ion of
secondary compression index
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The ultimate load-bearing capacity of a foundation, as well as the allowable
bearing capacity based on tolerable settlement considerations, can be effectively
determined from the field load test, generally referred to as the plate load test.
The plates that areused for tests in the field are usually made of steel and are
25 mm thick and 150 mm to 762 mm in diameter. Occasionally, square plates that
are 305 mm " 305 mm are also used.
o Field Load Test
( ) ( )pufu
qq =
( ) ( ) P
f
pufuB
B
qq =
( )
( )
plateofWidth:
foundationofWidth:
plateforcapacitybearingUltimate:
foundationforcapacitybearingUltimate:
p
f
pu
fu
B
B
q
qFor clay soi l :
For sand s oi l :
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Plate load test: (a) test arrangement;
(b) nature of load settlement curve
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p
f
pfB
B
SS =
2
2
+=
pf
f
pfBB
BSS
fS
pS
For clay:
For sand:
: Settlement of foundation
: Settlement of plate
Settlement relationships from plate load test:
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