Date post: | 22-Oct-2015 |
Category: |
Documents |
Upload: | sharmi1990 |
View: | 11 times |
Download: | 2 times |
NPTEL- Advanced Geotechnical Engineering
Dept. of Civil Engg. Indian Institute of Technology, Kanpur 1
Module 6
EVALUATION OF SOIL SETTLEMENT (Lectures 35 to 40)
Topics
1.1 INTRODUCTION
1.2 IMMEDIATE SETTLEMENT
1.2.1 Immediate Settlement from Theory of Elasticity
Settlement due to a concentrated point load at the surface
Settlement at the surface due to a uniformly loaded flexible circular area
Settlement at the surface due to a uniformly loaded flexible rectangular
area
Settlement of a flexible load area on an elastic layer of finite thickness
1.2.2 Settlement of rigid footings
1.2.3 Determination of Youngβs Modulus
1.2.4 Settlement Prediction in Sand by Empirical Correlation
1.2.5 Calculation of Immediate Settlement in Granular Soil Using Simplified
Strain Influence Factor
1.3 PRIMARY CONSOLIDATION SETTLEMENT
1.3.1 One-Dimensional Consolidation Settlement Calculation
Method A
Method B
1.3.2 Skempton-Bjerrum Modification for Calculation of Consolidation
Settlement
1.3.3 Settlement of Overconsolidated Clays
1.3.4 Precompression for Improving Foundation Soils
1.4 SECONDARY CONSOLIDATION SETTLEMENT
1.5 STRESS-PATH METHOD OF SETTLEMENT CALCULATION
1.5.1 Definition of Stress Path
NPTEL- Advanced Geotechnical Engineering
Dept. of Civil Engg. Indian Institute of Technology, Kanpur 2
1.5.2 Stress and Strain Path for Consolidated Undrained Undrained Triaxial
Tests
1.5.3 Calculation of Settlement from Stress Point
PROBLEMS
NPTEL- Advanced Geotechnical Engineering
Dept. of Civil Engg. Indian Institute of Technology, Kanpur 3
Chapter 6
Lecture 35
Evaluation of Soil Settlement -1
Topics
1.1 INTRODUCTION
1.2 IMMEDIATE SETTLEMENT
1.2.1 Immediate Settlement from Theory of Elasticity
Settlement due to a concentrated point load at the surface
Settlement at the surface due to a uniformly loaded flexible circular area
Settlement at the surface due to a uniformly loaded flexible rectangular
area
Summary of elastic settlement at the ground surface (z = 0) due to
uniformly distributed vertical loads on flexible areas
Settlement of a flexible load area on an elastic layer of finite thickness
1.1 INTRODUCTION
The increase of stress in soil layers due to the load imposed by various structures at the foundation level will
always be accompanied by some strain, which will result in the settlement of the structures. The various
aspects of settlement calculation are analyzed in this chapter.
In general, the total settlement S of a foundation can be given as
π = ππ + ππ + ππ (1)
Where
ππ = Immediate settlement
ππ = Primary consolidation settlement
ππ = Secondary consolidation settlement
NPTEL- Advanced Geotechnical Engineering
Dept. of Civil Engg. Indian Institute of Technology, Kanpur 4
The immediate settlement is sometimes referred to as the elastic settlement. In granular soils this is the
predominant part of the settlement, whereas in saturated inorganic silts and clays the primary consolidation
settlement probably predominates. The secondary consolidation settlement forms the major part of the total
settlement in highly organic soils and peats.
1.2 IMMEDIATE SETTLEMENT
1.2.1 Immediate Settlement from Theory of Elasticity
Settlement due to a concentrated point load at the surface
For elastic settlement due to a concentrated point load (figure 1), the strain at a depth z can be given in
cylindrical coordinates, by
Figure 1 Elastic settlement due to a concentrated point load
ππ§ =1
πΈ[ππ§ β π£ ππ + ππ ] (2)
Where E is the Youngβs modulus of the soil. The expressions for ππ§ ,ππ , and ππ are given in equations (53 to
55 from chapter 3), respectively. Substitution of these in equation (2) and simplification yields
ππ§ =π
2ππΈ
3(1+π£)π2π§
(π2+π§2)5/2 β3+π£ 1β2π£ π§
(π2+π§2)3/2 (3)
The settlement at a depth z can be found by integration equatin (3):
ππ = ππ§ ππ§ =π
2ππΈ
(1+π£)π§2
(π2+π§2)3/2 +2 1βπ£2
(π2+π§2)1/2
The settlement at the surface can be evaluated by putting z = 0 in the above equation:
NPTEL- Advanced Geotechnical Engineering
Dept. of Civil Engg. Indian Institute of Technology, Kanpur 5
ππ π π’πππππ =π
ππΈπ(1 β π£2) (4)
Settlement at the surface due to a uniformly loaded flexible circular area
The elastic settlement due to a uniformly loaded circular area (figure 2) can be determined by using the
same procedure as discussed for a point load, which involves determination of the strain ππ§ from the
equation and determination of the settlement by integration with respect to z.
Figure 2 Elastic settlement due to a uniformly loaded circular area
ππ§ =1
πΈ[ππ§ β π£(ππ + ππ)
Substitution of the relation for ππ§ ,ππ , and ππ in the preceding equation for strain and simplification gives
(Ahlvin and Ulery, 1962) where q is the load per unit area. Aβ and Bβ are nondimensional and are functions
of z/b and s/b; their values are given in table 7 and 8 in chapter 3.
ππ§ = π1+π£
πΈ[ 1 β 2π£ π΄β² + π΅β² ] (5)
The vertical deflection at a depth z can be obtained by integration of equation 6 as where πΌ1 = π΄β² and b is the
radius of the circular loaded area. The numerical values of πΌ2 (which is a function of z/b and s/b) are given in
table 1.
ππ = π1+π£
πΈπ
π§
ππΌ1 + (1 β π£)πΌ2 (6)
From equation (6) it follows that the settlement at the surface (i. e. , at z = 0) is
ππ = π π’πππππ ππ1βπ£2
πΈπΌ2 (7)
NPTEL- Advanced Geotechnical Engineering
Dept. of Civil Engg. Indian Institute of Technology, Kanpur 6
The term πΌ2 in equation (7) is usually referred to as the influence number. For saturated clays, we may
assume π£ = 0.5. so, at the center of the loaded area (i. e. , s/b = 0), πΌ2 = 2 and
ππ = π π’πππππ ππππ‘ππ =1.5ππ
πΈ=
0.75ππ΅
πΈ (8)
Table 1 Values of π°π π /π
π§/π 0 0.2 0.4 0.6 0.8 1 1.2 1.5 2
0 2.0 1.97987 1.91751 1.80575 1.62553 1.27319 .93676 .71185 .51671
0.1 1.80998 1.79018 1.72886 1.61961 1.44711 1.18107 .92670 .70888 .51627 0.2 1.63961 1.62068 1.56242 1.46001 1.30614 1.09996 .90098 .70074 .51382
0.3 1.48806 1.470044 1.40979 1.32442 1.19210 1.02740 .86726 .68823 .50966 0.4 1.35407 1.33802 1.28963 1.20822 1.09555 .96202 .83042 .67238 .50412
0.5 1.23607 1.22176 1.17894 1.10830 1.01312 .90298 .79308 .65429 .49728
0.6 1.13238 1.11998 1.08350 1.02154 .94120 .84917 .75653 .63469
0.7 1.04131 1.03037 .99794 .91049 .87742 .80030 .72143 .61442 .48061
0.8 .96125 .95175 .92386 .87928 .82136 .75571 .68809 .59398
0.9 .89072 .88251 .85856 .82616 .77950 .71495 .65677 .57361 1 .82843 .85005 .80465 .76809 .72587 .67769 .62701 .55364 .45122
1.2 .72410 .71882 .70370 .67937 .64814 .61187 .57329 .51552 .43013
1.5 .60555 ,60233 .57246 .57633 .55559 .53138 .50496 .46379 .39872 2 .47214 .47022 .44512 .45656 .44502 .43202 .41702 .39242 .35054
2.5 .38518 ,38403 .38098 .37608 .36940 .36155 .35243 .33698 .30913
3 .32457 .32403 .32184 .31887 .31464 .30969 .30381 .29364 .27453 4 .24620 .24588 .24820 .25128 .24168 .23932 .23668 .23164 .22188
5 .19805 .19785 .19455 .18450
6 .16554 .16326 .15750 7 .14217 .14077 .13699
8 .12448 .12352 .12112
9 .11079 .10989 .10854 10 .09900 .09820
After Ahlvin and Ulery (1962)
where π΅ = 2π is the diameter of the loaded area.
At the edge of the loaded area (π. π. , π§/π = 0and s/b = 1), I2 = 1.27 and
ππ = π π’πππππ ππππ = 1.27 0.75 ππ
πΈ= 0.95
ππ
πΈ=
0.475ππ΅
πΈ (9)
The average surface settlement is
ππ = π π’πππππ, ππ£πππππ = 0.85ππ(π π’πππππ, ππππ‘ππ) (10)
Settlement at the surface due to a uniformly loaded flexible rectangular area
The elastic deformation in the vertical direction at the corner of a uniformly loaded rectangular area of size
πΏ Γ π΅ can be obtained by proper integration of the expression for strain. The deformation at a depth z below
the corner of the rectangular area can be expressed in the form (Harr, 1966) π /π
π§/π 3 4 5 6 7 8 10 12 14
0 .33815 .25200 .20045 .16626 .14315 .12576 .09918 .08346 .07023
0.1 .33794 .25184 .20081
0.2 .33726 .25162 .20072 .16688 .14288 .12512 0.3 .33638 .25124
0.4
0.5 .33293 .24996 .19982 .16668 .14273 .12493 .09996 .08295 .07123 0.6
0.7
0.8 0.9
1 .31877 .24386 .19673 .16516 .14182 .12394 .09952 .08292 .07104
1.2 .31162 .24070 .19520 .16369 .14099 .12350 1.5 .29945 .23495 ..19053 .16199 .14058 .12281 .09876 .08270 .07064
2 .27740 .22418 .18618 .15846 .13762 .12124 .09792 .08196 .07026
NPTEL- Advanced Geotechnical Engineering
Dept. of Civil Engg. Indian Institute of Technology, Kanpur 7
2.5 .25550 .21208 .17898 .15395 .13463 .11928 .09700 .08115 .06980
3 .23487 .19977 .17154 .14919 .13119 .11694 .09558 .08061 .06897
4 .19908 .17640 .15596 .13864 .12396 .11172 .09300 .07864 .06848 5 .17080 .15575 .14130 .12785 .11615 .10585 .08915 .07675 .06695
6 .14868 .13842 .12792 .11778 .10836 .09990 .08562 .07452 .06522
7 .13097 .12404 .11620 .10843 .10101 .09387 .08197 .07210 .06377 8 .11680 .11176 .10600 .09976 .09400 .08848 .07800 .06928 .06200
9 .10548 .10161 .09702 .09234 .08784 .08298 .07407 .06678 .05976
10 .09510 .09290 .08980 .08300 .08180 .07710
ππ ππππππ =ππ΅
2πΈ(1 β π£2) πΌ3 β
1β2π£
1βπ£ πΌ4 (11)
Where πΌ3 =1
π πΌπ
1+π12+π1
2+π1
1+π12+π1
2βπ1
+ π πΌπ 1+π1
2+π12+1
1+π12+π1
2β1
(12)
πΌ4 =π1
ππ‘ππβ1
π1
π1 1+π12+π1
2 (13)
π1 =πΏ
π΅ (14)
π1 =π§
π΅ (15)
Values of πΌ3 and I4 are given in table 2.
For elastic surface settlement at the corner of a rectangular area, substituting π§/π = π1 = 0 in equation (11)
and make the necessary calculations; thus,
ππ ππππππ =ππ΅
2πΈ(1 β π£2)πΌ3 (16)
The settlement at the surface for the center of a rectangular area (figure 3) can be found by adding the
settlement for the corner of four rectangular areas of dimension πΏ/2 Γ π΅/2. Thus, from equation (11),
NPTEL- Advanced Geotechnical Engineering
Dept. of Civil Engg. Indian Institute of Technology, Kanpur 8
Figure 3 Determination of settlement at the center of a rectangular area of dimensions πΏ Γ π΅
ππ ππππ‘ππ = 4 π(π΅/2)
2πΈ (1 β π£2)πΌ3 =
ππ΅
πΈ(1 β π£2)πΌ3 (17)
The average surface settlement can be obtained as
ππ ππ£πππππ, π π’πππππ = 0.848ππ(ππππ‘ππ, π π’πππππ) (18)
Summary of elastic settlement at the ground surface (z = 0) due to uniformly
distributed vertical loads on flexible areas
For circular areas:
ππ = ππ΅ 1βπ£2
2πΈ πΌ2
Where
π΅ =Diameter of circular loaded area
πΌ2 = 2 (at center)
πΌ2 = 1.27(at edge)
πΌ2 = 0.85 Γ 2 = 1.7(average)
For rectangular areas, on the basic equations (16) to (18) we can write
ππ ππ΅
πΈ(1 β π£2) πΌ5 (19)
NPTEL- Advanced Geotechnical Engineering
Dept. of Civil Engg. Indian Institute of Technology, Kanpur 9
Where
πΌ5 = πΌ3(at center)
πΌ5 = 1
2πΌ3(at edge)
πΌ5 β 0.848πΌ3(average)
Table 3 gives the values of πΌ5 for various πΏ/π΅ ratios.
Settlement of a flexible load area on an elastic layer of finite thickness
For the settlement calculation, it was assumed that the elastic soil layer extends to an infinite depth.
However, if the elastic soil layer is underlain by a rigid incompressible base at a depth H (figure 4), the
settlement can be approximately calculated as
ππ = ππ(π§=0) β ππ(π§=π») (20)
Figure 4 Flexible loaded area over an elastic soil layer of finite thickness
Where ππ(π§=0) and ππ(π§=π»)are the settlements at the surface and at z = H, respectively.
Foundations are almost never placed at the ground surface, but at some depth π·π (figure 5). Hence, a
correction needs to be applied to the settlement values calculated on the assumption that the load is applied
at the ground surface. Fox (1948) proposed a correction factor for this which is a function of π·π/π΅, πΏ/π΅ and
Poissonβs ratio v. thus,
NPTEL- Advanced Geotechnical Engineering
Dept. of Civil Engg. Indian Institute of Technology, Kanpur 10
Figure 5 Average immediate settlement for a flexible rectangular loaded area located at a depth π·π from the
ground surface
πβ²π ππ£πππππ = πΌ6ππ(ππ£πππππ) (21)
Where
πΌ6 = correction factor for foundation depth, π·π
πβ²π = corrected elastic settlement of foundation
ππ = elastic settlement of foundation calculated on assumption that load is applied at ground surface
By computer programming of the equation proposed by Fox, Bowles (1977) obtained the values of πΌ6 for
various values of π·π/π΅ length-to-width ratio of the foundation, and Poissonβs ratio of the soil layer. These
values are shown in bfigure 6.
Table 3 Values of π°π πΌ5
πΏ/π΅ Center Corner Average
1 1.122 0.561 0.951 2 1.532 0.766 1.299
3 1.783 0.892 1.512
5 2.105 1.053 1.785 10 2.544 1.272 2.157
20 2.985 1.493 2.531 50 3.568 1.784 3.026
100 4.010 2.005 3.400
Janbu et al, (1956) proposed a generalized equation for average immediate settlement for uniformly loaded
flexible footings in the form
ππ ππ£πππππ = π1π0ππ΅
πΈ (forπ£ = 0.5) (22)
Where
NPTEL- Advanced Geotechnical Engineering
Dept. of Civil Engg. Indian Institute of Technology, Kanpur 11
π1 = Correction factor for finite thickness of elastic soil layer, H, as shown in figure 5.
π0 = Correction factor for depth of embankment of footing, π·π , as shown in figure 5.
π΅ = Width of rectangular loaded area of diameter of circular loaded area
Christian and Carrier (1978) made a critical evaluation of equation (22), the details of which will not be
presented here. However, they suggested that for π£ = 0.5, equation (22) could be retained for immediate
settlement calculations with a modification of the values of π1and ΞΌ2. The modified values of π1 are based
on the work of Groud (1972) and those for π0 are based on the work of Burland (1970). These are shown in
figure 7.. Christian and Carrier inferred that these values are generally adequate for circular and rectangular
footings.
Figure 6 Correction factor for the depth of embedment of the foundation. (Bowles 1977)
Figure 7 Improved chart for use in equation (22). (After Christian and Carrier 1978)
NPTEL- Advanced Geotechnical Engineering
Dept. of Civil Engg. Indian Institute of Technology, Kanpur 12
Another general method for estimation of immediate settlement is to divide the underlying soil into π layers
of finite thicknesses (figure 5). It the strain at the middle of each layer can be calculated. The total
immediate settlement can be obtained as where βπ§(π) is the thickness of the ππ‘π layer and ππ§(π) is the vertical
strain at the middle of the ππ‘π layer.
ππ = βπ§(π)ππ§(π)π=ππ=1 (23)
The method of using equation (23) is demonstrated in example 2.