1. 15. IS6403:1981METHOD
67
…..EQ.55
If the water table is at or below a depth of Df +B,
measured from the ground surface, w’=1. If the water
table rises to the base of the footing or above, w’=0.5. If
the water table lies in between then the value is obtained
by linear interpolation. The shape factors give
n
by
Hansen and inclination
used.
factors as given by Vesi
c
are
3. 16. EFFECTOFWATERTABLEON
BEARING CAPACITY
Water in soil is known to affect its unit weight and
also the shearparameters cand φ.
When the soil is submerged under water, the
effective unit weight γ′ is to be used in the computation of
bearing capacity.
NOTE:
Effective unit weight γ′ is roughly half the saturated
unit weight; consequently there will be about 50%
reduction in the value of the corresponding term in the
bearing capacity formula.
69
4. •If the water table isat the level of the base of the footing,
γ′ isto be usedfor γ in the third term, a reduction factor
of 0.5 isto be applied to the third term.
•For any location of the water table intermediate
between the base of the footing and a depth equal to
the width of the footing below its base, a suitable linear
interpolation of the necessaryreduction is suggested.
third term
• If the water table is above the base of the
is
footing, the reduction factor for the
obviously limited to the maximum of 0.5.
5. •The maximum reduction of 0.5 is indicated for the
second term when the water table is at the ground level
itself (or above it), since γ′ is to be used for γ in the
second term.
•While no reduction in the secondterm is required when
the water table isat or below thebase of thefooting,
•Inthe caseof purely cohesivesoils,sinceφ ≈ 0°,
Nq= 1 andNγ = 0,
•Net ultimate bearing capacity isgiven by c.Nc, which
isvirtually unaffected by the water table, if it is below
the base of the footing.
6. For locations of ground water table within a depth of the
width of the foundation below the base and the ground
level, the equation for the ultimate bearing capacity may
be modified as follows:
...(Eq. 56)
*appropriate multiplying factor shouldbe usedfor isolated footings.
**Appropriate shape factor.
• If the water table isat the groundlevel, only the
gross bearing capacity is reduced by 50% of the
surcharge term γ.Df (Nq = 1), while the net value is again
only c. Nc.
• Inthe caseof purely cohesionlesssoils, since
c= 0, andφ > 0, andNqandNγ are significantly high,
8. ...(Eq. 57)
...(Eq. 58)
Note.
•Forzq> Df(the water table isbelowthebaseof the
footing), Rqislimitedto1.0.
•For0 ≤ zq≤ Df(the water table isabovethebase of the
footing), Rγislimitedto0.5.
•for zq> (Df+ b)or zγ > b,Rqaswell asRγare
limitedto1.0.
•Forzq= 0, Rqaswell asRγare limitedto0.5.
9. 18. CONTACTPRESSURE
‘Contact pressure’isthe actual pressuretransmitted from the foundation
to the soil.
Auniformly loaded foundation will not necessarily transmita uniform
contact pressure to the soil. This is possibleonly if the foundation is
perfectly ‘flexible’;
89
10. 19. PLATELOAD TEST
test essentially consists in loading
level, increasing the load in arbitrary increments,
The
foundation
determining the settlements corresponding to each load after
a rigid plate at the
and
the
settlement hasnearly ceased eachtime a load increment isapplied.
The nature of the load applied may be gravity loading or dead
weights on an improvised platform or reaction loading by using a
hydraulic jack. Thereaction of the jack load is taken by a cross beam or a
steel trussanchored suitably at both ends.
T
estplates are usually square or circular, the sizeranging from 300
to 750 mm(side or diameter); the minimumthicknessrecommended is 25
mmfor providing sufficient rigidity.
Jack-loading issuperior in termsof accuracy and uniformity of
loading. Settlementof the test plate ismeasured by meansof at least two
or three dial gaugeswith a least countof 0.02 mm.
90
12. Thetest pit should be at least five times as wide asthe test plate and the
bottom of the test plate should correspond to the proposed foundation
level. At the centre of the pit, a small square hole is made the size being
that of the testplate and the depth being suchthat,
...(Eq. 64)
13. Bigger sizeplates are preferred in cohesivesoils.Thetest procedure is
given in IS:1888–1982 (Revised).Theprocedure, in brief, isasfollows:
(i)After excavating the pit of required size and levelling the base, the test
plate is seated over the ground. Alittle sand may be spread below the
plate for even support. If ground water is encountered, it should be
lowered slightly below the base by meansof pumping.
(ii)A seating pressure of 7.0 kN/m2 (70 g/cm2) is applied and released
before actual loading is commenced.
(iii)The first increment of load, say about one-tenth of the anticipated
ultimate bearing capacity, is applied. Settlements are recorded with the
aid of the dial gauges after 1 min., 4 min., 10 min., 20 min., 40 min.,
and 60 min., and later on at hourly intervals until the rate of settlement
islessthan 0.02 mm/hour,or at least for 24 hours.
14. (iv) Thetest is continued until a load of about 1.5 times the anticipated
ultimate load is applied. According to another school of thought, a
settlement at which failure occurs or at least 2.5 cms should be
reached.
(v) Fromthe results of the test, a plot should be made between pressure
and settlement, which is usually referred to as the ‘‘load- settlement
curve’’, rather loosely. The bearing capacity is determined from this
plot, whichisdealt with in thenext
subsection.
Load-Settlement Curves
Load-Settlement curves or pressure-settlement curves to be
more precise, are obtained as a result of loading tests either in the
laboratory or in the field, oedometer tests being an example in the
laboratory and plate bearingtest,in the field.
15. Curve I is typical of dense
sandor gravelor stiffclay,
wherein general shear
failureoccurs.
Curve II is typical of loose
sand or soft clay, wherein
localshearfailure occurs.
Curve III is typical of
many c – φ soils which
exhibit characteristics
intermediate between the
above two.
16. Determination of bearing capacity from plate load test
(Terzaghi and Peck, 1948):
...(Eq. 65)
S= settlementof theproposed foundation (mm),
Sp= settlementof thetestplate(mm),
b = sizeof theproposedfoundation (m), and
bp = sizeof thetestplate (m).
Thisisapplicable for sands.
17. Therelationship issimpler for clays,sincethe modulus value
Es,for claysisreasonably constant:
...(Eq. 66)
Sp= Settlementof a testplate of 300 mmsquaresize, and
S= Settlementof a footing of width b.
The method for the determination of the bearing capacity of a footing
of width b should be apparent now. The permissible settlement value,
such as 25 mm, should be substituted in the equation that is applicable
(Eq.50 to 51) ; and the Sp,thesettlementof theplate mustbe calculated.
From the load-settlement curve, the pressure corresponding to the
computed settlement Sp, is the required value of the ultimate 9
b7earing
capacity,qult, for thefooting.
18. Limitations of Plate Load Tests
(i)Size(plate) effectsare veryimportant.
(ii)Consolidation settlementsincohesivesoils,whichmaytake
years,cannotbe predicted,
(iii)Resultsfrom plate load testare not recommendedto be
usedfor thedesignof stripfootings,
(iv)The load test results reflect the characteristics of the soil
located only within a depth of about twice the width of the
plate.
Thus,it may be seenthat interpretation and useof the plate
load test results requires great care and judgment, on the
part of the foundation engineer.
19. 20. BEARINGCAPACITYFROM
PENETRATION TESTS
Terzaghi and Peck have prepared charts for allowable
bearing pressure, based on a standard allowable
settlement, for footings of knownwidths onsand, whose N-
valuesareknown.
99
20. obtainedfromthe charts.
Above figures do not apply to gravels or those soils containing a large
percentage of gravels. These charts have been prepared on the
assumption that the water table is at a depth greater than the width of
the footing below the base of the footing. If the water table is located at
t
1
h
0
e
0 baseof thefooting, the allowable pressureistaken ashalf that
21. Charts given by Peck, Hanson and Thornburn (1953) may be used
for the determination of allowable bearing pressure for a specific
allowable settlement of 25 mmor 40 mm,
Fig.1 allowable bearing pressure
for 40mm settlement.
Fig.2 allowable soil pressure
22. Teng(1969) hasproposed the following equation for the graphical
relationship of Terzaghi and Peckfor a settlement of 25 mm:
...(Eq. 67)
where qna= netallowable soil pressurein kN/m2 for a settlement
of 25 mm,
N = Standard penetration valuecorrectedfor overburdenpressure
andother applicable factors,
b = width of footing in metres,
Rγ= correction factor for location of water table, (Eq.56)
and Rd= Depthfactor (= 1 + Df /b) ≤ 2.
whereDf = depthof footing inmetres.
Themodified equation of T
engisasfollows:
...(Eq.68)
23. Meyerhof (1956) has proposed slightly different equations for a
settlement of 25 mm, but these yield almost the same results as T
eng’s
equation:
...(Eq.69)
...(Eq.70)
Modified equation of Meyerhof isas follows:
...(Eq.71)
...(Eq.72)
24. TheI.S.codeof practice gives Eq.73 for a settlementof 40 mm;but,
it doesnot consider the depth effect.
...(Eq. 73)
...(Eq.73a)
qna= netallowable soil pressureinkN/m2 for a settlement of
25 mm,
N = Standard penetration value corrected for
overburden pressureandother applicablefactors,
b = width of footing inmetres,
Rγ= correction factor for location of water table, (Eq.52)
Rd= Depthfactor (= 1 + Df /b) ≤ 2.
Df = depthof footing in metres.
25. Teng(1969) also givesthe following equations for bearing
capacityof sandsbased onthe criterion of shearfailure:
...(Eq. 74)
...(Eq. 75)
N = Standard penetration value, after applying the necessary
corrections,
b = width of continuous footing (side, if square, and diameter, if
circular in metres),
Df = depthof footing in metres,and
RγandRq= correction factors for theposition of theground water
table, defined in Eqs.52 & 53.
27. QUICK NOTE
Skempton’s equations are preferred for rectangular footings in pure
clay.
Correlation of cohesion and consistency of clays with N-values is not
reliable. Unconfined compression test is recommended for evaluating
cohesion.
Overconsolidated or precompressedclays might showhair cracksand
slickensides.Load testsare recommended in suchcases.
Settlementsof footings in clays maybe calculated or predicted by the
useof Terzaghi’sone-dimensionalconsolidation.
Thebearing capacity of footings in clays ispractically unaffected by
the sizeof thefoundation.
28. Example1: Compute the safe bearing capacity of a square footing 1.5 m
× 1.5 m, located at a depth of 1 mbelow the ground level in a soil of
average density 20 kN/m3. φ = 20°, Nc = 17.7, Nq = 7.4, and Nγ
= 5.0. Assumea suitable factor of safety and that the water table is very
deep. Also compute the reduction in safe bearing capacity of the
footing if the water table risesto the ground level.
b = 1.5 mSquarefooting Df = 1 m
γ= 20 kN/m3 φ = 20° Nc= 17.7, Nq = 7.4, andNγ =5.0
Assumec= 0 andη = 3
qult = 1.3 cNc+ 0.4 γ b Nγ +γDf Nq = 0.4 γ b Nγ +γ Df Nq, in this
case.
= 0.4 × 20 × 1.5 × 5.0 + 20 × 1 × 7.4 = 60 + 148 = 208 kN/m2
qnetult = qult – γ Df = 208 – 20 × 1 = 188 kN/m2
30. Example2:Aplate load testwasconductedona uniform depositof sand
andthefollowing data wereobtained:
(i)Plot thepressure-settlementcurveanddeterminethefailure stress.
(ii)A square footing, 2m × 2 m, is to be founded at 1.5 mdepth in this
soil. Assuming the factor of safety against shear failure as 3 and the
maximum permissible settlement as 40 mm, determine the allowable
bearing pressure.
(iii) Designof footing for a load of 2,000 kN, if thewater table isat
a great depth.
31. (i) The pressure-settlement curve is shown in Fig. Thefailure point is
obtained asthe point corresponding to the intersection of the initial
and final tangents. Inthiscase,the failure stressis500kN/m2.
∴qult = 500 kN/m2
32. (ii) Thevalueof qult hereisgiven by
0.5.γbp Nγ .
bp, thesizeof testplate = 0.75 m
Assumingγ= 20kN/m3,
500 = 0.5 × 20 × 0.75Nγ
∴Nγ =500/7.5 ≈ 6.7
φ = 38°
∴Nq ≈ 50 from Terzaghi’s charts.
Forsquare footing of size2 mand Df = 1.5 m,
qnetult = 0.4 γ b Nγ +γDf (Nq –1)
= 0.4 × 20 × 2 × 67 + 20 × 1.5 × 49 = 2,542 kN/m2
qsafe= 2542/3 ≈ 847 kN/m2 (for failure againstshear)
33. Pressure for a settlement of 27 mm for the plate (from Fig. ) = 550
kN/m2. Allowable bearing pressure is the smaller of the values from
the two criteria = 550 kN/m2.
(iii) Designload = 2,000kN
FromPart (ii), it isknownthat a 2 msquarefooting cancarry a load of
2 × 2 × 550 = 2,200 kN.
Therefore, a 2 m square footing placed at a depth of 1.5 m is
adequate for thedesignload.
34. 114
Example3 (ESECE2017)
In a plate load test on a soil, at a particular magnitude of the
settlement, it was observed that the bearing pressure beneath the footing
is 100 kN/m2 and the perimeter shear is 25 kN/m2. Correspondingly, the
load capacity of a 2msquare footing at the samesettlement will be
(a) 200 kN
(c)400kN
(b) 300 kN
(d) 600 kN
Sol.
Q = Aσb + Pσs
σb = Bearingpressure
σs= Perimetershear
A= Plate base area
P= Perimeter
Q = Loadcapacity
Q = 2 × 2 × 100 + 2 × 4 × 25
Q = 600 kN
35. GATE2018 :Thecontactpressureand settlementdistribution
for a footing are shownin the figure. Thefigure correspondsto
a
(a) rigid footing ongranular soil
(b) flexible footing ongranular soil
(c)flexible footing onsaturated clay
(d) rigid footing oncohesivesoil.
36. REFRENCES:
C. VENKATARAMAIAH
GEOTECHNICAL ENGINEERING
THIRD EDITION
( NEW AGE INTERNATIONAL (P) LTD. PUBLISHERS)
MUNI BUDHU-
SOIL MECHANICS AND FOUNDATIONS
THIRD EDITION -WILEY (2010)
A.S.R RAO & GOPAL RANJAN-
BASIC AND APPLIED SOIL MECHANICS
(NEW AGE INTERNATIONAL (P) LTD., PUBLISHERS)
IS 6401:1981 & IS: 1888–1982
