BEARING CAPACITY OF

SOIL ByM Firdaus, MT

www.dauspoli.co.cc

CONCEPT • Foundation width (B) lied on the ground covered with sand layer. If

foundation receives uniform load (q) per square, the foundation will be in under displacement condition.

• Foundation displacement will be increased as the load is increased. If the value of q equal to value of qu is achieved, the failure of subgrade end bearing will happen even though there is no additional load (q).

Types of subgrade end bearing failure

Analisis Terzaghi• Developing plastic failure theory for strapp footing analysis;

Ratio value of length (L) compared to foundation width (B) is more than 5, and shallow foundation is depth value (Df) which is equal or less than the width value (B).

• (General Shear failure):strapp : (B-width)square : (B-minimum)circle : (B-circle diametre)

• (local shear failure) by changing the value c = c’ = 2/3.c and tanφ’ = 2/3. tanφ, as the follows:

strapp : (B-width)square : (B-minimum)circle : (B-circle diametre)

NBNqNcq

NBNqNcq

NBNqNcq

qcu

qcu

qcu

...3,0...3,1

...4,0...3,1

...21..

'...3,0'.''..3,1

'...4,0'.''..3,1

'...21'.''.

NBNqNcq

NBNqNcq

NBNqNcq

qcu

qcu

qcu

Terzaghi’s Table for Subgrade End Bearing Coefficient

Graphic of Subgrade End Bearing Coefficient in Semi-Logarithm Scale

70,14:1 1 Lap

68,15:2 2 Lap

7,14;25;68,17:3 3 cLap

90,4;30;/66,16:4 34 cmkNLap

0,8

1,00

1,20

1,10

2,3

Foundation on Ground with Several Layers

2211 .. DfDfq

68,15.170,14.80,0 2/44,27 mkNq

Parameter ø,c & γ which is used in Terzaghi formula; the average value taken for measurement is the same as foundation width value.

The value below foundation taken is 2,3 m, and so

39,27

)1,120,1(

30.1,125.2,1.

i

iirt h

h

i

iirt h

chc

.2/01,10

)10,120,1(

90,4.1,17,14.2,1mkN

i

iirt h

h

.2/17,17

)10,120,1(

66,16.1,164,17.2,1mkN

For : ø = 27,39⁰ → interpolated, show the result :

40,14

38,17

88,30

N

N

N

q

c

For square footing : NBNqNccult qnt ...4,0)1(..3,1

40,14.17,17.3,2.40,0)138,17(44,2788,30.01,10.3,1 ntult

2/78,1078

47,22747,44984,401

mkNult

ult

nt

nt

2/59,3593

78,1078mkNallnt

2/03,38744,2759,359 mkNbrutto

1:1 Lap

'2:2 Lap

'

Df1

Df2

FOUNDATION ON MULTIPLE SOIL LAYER WITH UNDER POSITION OF GROUND WATER LEVEL

'211 .. DfDfq

Square :

ShearGeneralNBNqNcult qcnt ...4,0)1(..3,1 '

ShearLocalNBNqNcult qcnt''''' ...4,0)1(..3,1

Df1

1,50

2,50

4 m

1

;;2 c

;;'3 c

CIRCLE FOUNDATION WITH GROUND WATER LEVEL UNDER THE BASE OF FOUNDATION

Where : ø; c & γ used from averaging.

)50,250,1(

50,2.50,1. '1

rt

If ground water level under the foundation < B,Ground water level have influences.

ShearGeneralNBNqNcult rtqcrtnt ...3,0)1(..3,1

ShearLocalNBNqNcult rtqcrtnt'''' ...3,0)1(..3,1

If depth of ground water level under the foundation > B, ground water level denied

Safety Factor• Safety factor used for calculate of allowable bearing capacity

(qijin) of foundation• General condition, SF taken around 2 – 3 and critical condition

actually taken around 3 - 4• Allowable bearing capacity (qijin) = qu/SF

• qall = qu/SF = , A = found. load area

• qnet = qijin netto = (qu – q)/SF , where q = γ.Df

• qijin netto = W(D+L)/A

SFAWWW sFLD //)(

ExampleStrapp footing with soil characteristics : γ = 18 kN/m3, φ = 28°dan c =15 kN/m2. Determine the allowable bearing capacity (qall) :

a) General shear failure condition:From terzaghi bearing capacity table for φ = 28° Nc = 32, Nγ= 16, Nq = 18. q = γ.Df= 18 . 0,80 = 14,4 kN/m2, use formula :

2

2

/8,2204/2,883

/2,88316.0,1.18.5,018.4,1432.15

mkNq

mkNq

all

u

b) Local shear failure condition:local shear : c’ = 2/3.c = 10 kN/m2

for φ = 28° Nc’ = 18; Nγ’= 4,5; Nq’ = 7.

q = γ.Df = 14,4 kN/m2, use formula :

2

2

/3,804/5,321

/5,3215,4.0,1.18.5,07.4,1418.10

mkNq

mkNq

all

u

Meyerhof Analysis, Debeer & Vesic

Zona I is an active area (rankine), zona II is area of radial shear, and zona III is a pasive area (rankine)

Bearing capasity of stapp footing : qu = qc + qq + qγ

Bearing capacity table, vesic

bearing capacity soil formula besides strapp footing type

Where : sc, sq, sγ : shape factor

dc, dq, dγ : depth factor

ic, iq, iγ : tilt factor

a) Shape factor1. Strapp footing (B : wide; L : length)

2. Square and circle footing

NBidsNidsqNidscq qqqqccccu .............

L

Bs

L

Bs

N

N

L

Bs q

c

qc 4,01;tan1;1

6,0;tan1;1

ssN

Ns q

c

qc

b) Depth factor1) Ratio Df/B ≤ 1

if φ = 0,

2) Ratio Df/B > 1

If φ = 0,

1;)sin1(tan21;tan

1 2

d

B

Dd

N

ddd f

qq

qqc

B

Dd f4,01

1;)sin1(tan21;tan

1 2

d

B

Dd

N

ddd f

qq

qqc

B

Dd f1tan4,01

c) Tilt factor

α is a resultant of angle of force where work straight vertically

2

2

1

901

i

ii qc

ExampleCalculate allowable bearing capacity of square footing with 1,2

m wide for factor safety (SF) = 3Soil characteristics :γ = 17 kN/m3

φ = 20°c = 20 kN/m2

Completion :

NBidsNidsqNidscq qqqqccccu ......5,0........

a) Tilt factorvertical load resultant, define ic = iq = iγ = 1, become :

b) Soil bearing capacity factorφ = 20°, vesic table : Nc = 30,14; Nq = 18,40; Nγ = 22,40

c) Shape factorsquare footing B = L = 1,2 m

NBdsNdsqNdscq qqqcccu .....5,0......

6,0

364,1tan1

610,1/1

s

s

NNs

q

cqc

d) Depth factorDf/B = 1,2/1,2 = 1 ≥ 1, use formula :

e) Uniform load (1,2 m depth of foundation)q = 1,2.17 = 20,40 kN/m2

Ultimate bearing capacity :

SF = 3, so qijin = qu/SF = 710,73 kN/m2

Allowable total load of foundation = A.qijin = 1023,45 kN

1

362,1)tan./()1(

315,1/.)sin1(tan21 2

d

Nddd

BDd

qqqc

fq

2/188,2132

4,22.2,1.17.1.6,0.5,04,18.315,1.364,1.4,2014,30.362,1.61,1.20

.....5,0......

mkNq

q

NBdsNdsqNdscq

u

u

qqqcccu