74
Bearing Capacity ري ب ار ب ت ي ف ر ظ

Bearing Capacity ظرفيت باربري. Footing Shallow Foundations

Embed Size (px)

Citation preview

Page 1: Bearing Capacity ظرفيت باربري. Footing Shallow Foundations

Bearing Capacity

ظرفيت باربري

Page 2: Bearing Capacity ظرفيت باربري. Footing Shallow Foundations

Footing

Shallow Foundations

Page 3: Bearing Capacity ظرفيت باربري. Footing Shallow Foundations

Footing

Shallow Foundations

Page 4: Bearing Capacity ظرفيت باربري. Footing Shallow Foundations

Shallow Foundations

D

B

QTypical Buried Footing

Page 5: Bearing Capacity ظرفيت باربري. Footing Shallow Foundations

Shallow Foundations

D

B

Q

qs = DQ

Typical Buried Footing

Equivalent Surface Footing

Page 6: Bearing Capacity ظرفيت باربري. Footing Shallow Foundations

Shallow Foundations

D

B

Q

qs = DQ

Typical Buried Footing

Equivalent Surface Footing

Shallow Foundations have D/B < 1

Page 7: Bearing Capacity ظرفيت باربري. Footing Shallow Foundations

Methods of analysis

•Lower bound approach–failure stress state in equilibrium

–failure load less than or equal to true collapse

•Upper bound approach–failure mechanism assumed

–failure load greater than or equal to true collapse

Shallow Foundations

Page 8: Bearing Capacity ظرفيت باربري. Footing Shallow Foundations

Shallow Foundations

q f

Footing

Surcharge q s

Page 9: Bearing Capacity ظرفيت باربري. Footing Shallow Foundations

Shallow Foundations

q f

Footing

Surcharge q s

H

Frictionless Discontinuity

Page 10: Bearing Capacity ظرفيت باربري. Footing Shallow Foundations

Shallow Foundations

q f

Footing

Surcharge q s

Soil at stateof ActiveFailure with v > h

H

Frictionless Discontinuity

Page 11: Bearing Capacity ظرفيت باربري. Footing Shallow Foundations

Shallow Foundations

q f

Footing

Surcharge q s

Soil at stateof ActiveFailure with v > h

H

Frictionless Discontinuity 1 3 2 N c N

Page 12: Bearing Capacity ظرفيت باربري. Footing Shallow Foundations

Shallow Foundations

q f

Footing

Surcharge q s

Soil at stateof ActiveFailure with v > h

Soil at stateof PassiveFailure with h > v

H

Frictionless Discontinuity 1 3 2 N c N

Page 13: Bearing Capacity ظرفيت باربري. Footing Shallow Foundations

Shallow Foundations

q f

Footing

Surcharge q s

Soil at stateof ActiveFailure with v > h

Soil at stateof PassiveFailure with h > v

H

Frictionless Discontinuity 1 3 2 N c N N

c

c

1

3

cot

cot

Page 14: Bearing Capacity ظرفيت باربري. Footing Shallow Foundations

Shallow Foundations

v = 1

h = 3

h = 1

v = 3

Page 15: Bearing Capacity ظرفيت باربري. Footing Shallow Foundations

Shallow Foundations

v fq z

v = 1

h = 3

h = 1

v = 3

v sq z

Page 16: Bearing Capacity ظرفيت باربري. Footing Shallow Foundations

Shallow Foundations

v fq z

v = 1

h = 3

Nq z c

cf

h

cot

cot

h = 1

v = 3

v sq z

Nc

q z ch

s

cot

cot

Page 17: Bearing Capacity ظرفيت باربري. Footing Shallow Foundations

Shallow Foundations

v fq z

v = 1

h = 3

Nq z c

cf

h

cot

cot

h fNq z c c

1( cot ) cot

h = 1

v = 3

v sq z

Nc

q z ch

s

cot

cot

h sN q z c c ( cot ) cot

Page 18: Bearing Capacity ظرفيت باربري. Footing Shallow Foundations

Shallow Foundations

( ) ( ) h active h passive

HH

dz dz 00

Page 19: Bearing Capacity ظرفيت باربري. Footing Shallow Foundations

Shallow Foundations

( ) ( ) h active h passive

HH

dz dz 00

1

2 2

2 2

Nq H

Hc H N q H

Hc Hf s

cot cot

Page 20: Bearing Capacity ظرفيت باربري. Footing Shallow Foundations

Shallow Foundations

( ) ( ) h active h passive

HH

dz dz 00

1

2 2

2 2

Nq H

Hc H N q H

Hc Hf s

cot cot

q q NH

N c Nf s

2 2 2

21 1cot

Page 21: Bearing Capacity ظرفيت باربري. Footing Shallow Foundations

•This solution will give a lower bound to the true solution because of the simplified stress distribution assumed in the soil

•Similar terms occur in all bearing capacity expressions. They are functions of the friction angle and

•the surcharge applied to the soil surface

•the self weight of the soil

•cohesion

Shallow Foundations

q q NH

N c Nf s

2 2 2

21 1cot

Page 22: Bearing Capacity ظرفيت باربري. Footing Shallow Foundations

•A general bearing capacity equation can be written

Shallow Foundations

q q NB

N c Nf s q c

2

Page 23: Bearing Capacity ظرفيت باربري. Footing Shallow Foundations

•A general bearing capacity equation can be written

•The terms Nq, N and Nc are known as the bearing capacity factors

Shallow Foundations

q q NB

N c Nf s q c

2

Page 24: Bearing Capacity ظرفيت باربري. Footing Shallow Foundations

•A general bearing capacity equation can be written

•The terms Nq, N and Nc are known as the bearing capacity factors

•Values can be determined from charts

Shallow Foundations

q q NB

N c Nf s q c

2

Page 25: Bearing Capacity ظرفيت باربري. Footing Shallow Foundations

Shallow Foundations

BEARING CAPACITY FACTORS [After Terzaghi and Peck (1948)]

60 50 40 30 20 10 0 20 40 60 80

N and N

0

10

20

30

40

(deg

rees

)

q c N

NN q

B

Da

bc

d

q= D

Q f

ff

Bearing capacity of a shallow foundation

ULTIMATE BEARING CAPACITY OF CLAY ( = 0 only) (After A.W. Skempton)

0 1 2 3 4 5

D/B

5

6

7

8

9

Nc

5.14

B

D

N (for rectangle)

= (0.84+0.16 ) N (square)

L= Length of footing

BL c

q = cNcult

q = B N + cN + D N continuous footing12f c f q

q = 0.4 BN + 1.3cN + D N squaref c f q

q = 0.6 RN + 1.3cN + D N circularf c f q

q = cN + Df c

c

Nc

BEARING CAPACITY THEORIES OF TERZAGHI AND SKEMPTON

Page 26: Bearing Capacity ظرفيت باربري. Footing Shallow Foundations

Dq= D

Qf

ff

B

Shallow Foundations

Mechanism analysed by Terzaghi

Page 27: Bearing Capacity ظرفيت باربري. Footing Shallow Foundations

Effect of Foundation Shape

q q NB

N c Nf s q c

2

Continuous strip footing

Page 28: Bearing Capacity ظرفيت باربري. Footing Shallow Foundations

Effect of Foundation Shape

q q NB

N c Nf s q c

2

q q N BN c Nf s q c 0 13.4 .

Continuous strip footing

Square footing

Page 29: Bearing Capacity ظرفيت باربري. Footing Shallow Foundations

Effect of Foundation Shape

q q NB

N c Nf s q c

2

q q N BN c Nf s q c 0 13.4 .

q q N BN c Nf s q c 0 6 13. .

Continuous strip footing

Square footing

Circular footing

Page 30: Bearing Capacity ظرفيت باربري. Footing Shallow Foundations

•Effective stress analysis is needed to assess the long term foundation capacity .

•Total and effective stresses are identical if the soil is dry. The analysis is identical to that described above except that the parameters used in the equations are c´, ´, dry

rather than cu, u, sat .

•If the water table is more than a depth of 1.5 B (the footing width) below the base of the footing the water can be assumed to have no effect.

Effective Stress Analysis

Page 31: Bearing Capacity ظرفيت باربري. Footing Shallow Foundations

•If the soil below the base of the footing is saturated, the analysis must account for the water pressures.

Effective Stress Analysis

Page 32: Bearing Capacity ظرفيت باربري. Footing Shallow Foundations

•If the soil below the base of the footing is saturated, the analysis must account for the water pressures.

Effective Stress Analysis

qs = D

Q = q f B

u = u o

Page 33: Bearing Capacity ظرفيت باربري. Footing Shallow Foundations

•If the soil below the base of the footing is saturated, the analysis must account for the water pressures.

Effective Stress Analysis

qs = D

Q = q f B

u = u o

Page 34: Bearing Capacity ظرفيت باربري. Footing Shallow Foundations

•If the soil below the base of the footing is saturated, the analysis must account for the water pressures.

Effective Stress Analysis

qs = D

Q = q f B

u = u o

Page 35: Bearing Capacity ظرفيت باربري. Footing Shallow Foundations

•If the soil below the base of the footing is saturated, the analysis must account for the water pressures.

Effective Stress Analysis

qs = D

Q = q f B

u = u o

Page 36: Bearing Capacity ظرفيت باربري. Footing Shallow Foundations

Effective Stress Analysis

These effective quantities are required because Mohr Coulomb failure criterion must be expressed in terms of effective stress

Nc

c

1

3

cot

cot

Page 37: Bearing Capacity ظرفيت باربري. Footing Shallow Foundations

Effective Stress Analysis

These effective quantities are required because Mohr Coulomb failure criterion must be expressed in terms of effective stress

Nc

c

1

3

cot

cot

The total vertical stress, pore pressure and effective vertical stress at any depth z beneath the footing are

Page 38: Bearing Capacity ظرفيت باربري. Footing Shallow Foundations

Effective Stress Analysis

These effective quantities are required because Mohr Coulomb failure criterion must be expressed in terms of effective stress

Nc

c

1

3

cot

cot

The total vertical stress, pore pressure and effective vertical stress at any depth z beneath the footing are

Page 39: Bearing Capacity ظرفيت باربري. Footing Shallow Foundations

Effective Stress Analysis

These effective quantities are required because Mohr Coulomb failure criterion must be expressed in terms of effective stress

Nc

c

1

3

cot

cot

The total vertical stress, pore pressure and effective vertical stress at any depth z beneath the footing are

Page 40: Bearing Capacity ظرفيت باربري. Footing Shallow Foundations

Effective Stress Analysis

v fq z

’v = ’1

’h = ’3

Nq z c

cf

h

cot

cot

h fN

q z c c1

( cot ) cot

v sq z

Nc

q z ch

s

cot

cot

h sN q z c c( cot ) cot

’h = ’1

’v = ’3

Page 41: Bearing Capacity ظرفيت باربري. Footing Shallow Foundations

Effective Stress Analysis

q q NH

N c Nf s

2 2 2

21 1cot

The simple analysis leads to

Page 42: Bearing Capacity ظرفيت باربري. Footing Shallow Foundations

Effective Stress Analysis

q q NH

N c Nf s

2 2 2

21 1cot

The simple analysis leads to

This is similar to the previous expression except that now all terms involve effective quantities.

Page 43: Bearing Capacity ظرفيت باربري. Footing Shallow Foundations

Effective Stress Analysis

q q NH

N c Nf s

2 2 2

21 1cot

q q NB

N c Nf s q c

2

The simple analysis leads to

This is similar to the previous expression except that now all terms involve effective quantities.

As before a general expression can be written with the form

Page 44: Bearing Capacity ظرفيت باربري. Footing Shallow Foundations

Effective Stress Analysis

q q NH

N c Nf s

2 2 2

21 1cot

q q NB

N c Nf s q c

2

The simple analysis leads to

This is similar to the previous expression except that now all terms involve effective quantities.

As before a general expression can be written with the form

The Bearing Capacity Factors are identical to those from Total Stress Analysis

Page 45: Bearing Capacity ظرفيت باربري. Footing Shallow Foundations

Effective Stress Analysis

q q NH

N c Nf s

2 2 2

21 1cot

q q NB

N c Nf s q c

2

The simple analysis leads to

This is similar to the previous expression except that now all terms involve effective quantities.

As before a general expression can be written with the form

The Bearing Capacity Factors are identical to those from Total Stress Analysis

Note that the Total Bearing Capacity qf = q’f + uo

Page 46: Bearing Capacity ظرفيت باربري. Footing Shallow Foundations

Analysis has so far considered

•soil strength parameters

•rate of loading (drained or undrained)

•groundwater conditions (dry or saturated)

•foundation shape (strip footing, square or circle)

Other important factors include

•soil compressibility

•embedment (D/B > 1)

•inclined loading

•eccentric loading

•non-homogeneous soil

Effective Stress Analysis

Page 47: Bearing Capacity ظرفيت باربري. Footing Shallow Foundations

•More theoretically accurate bearing capacity factors are given on pages 69 to 71 of the Data Sheets

•In practice the Terzaghi factors are still widely used .

•The bearing capacity equation assumes that the effects of c', , and ' can be superimposed .

•This is not correct as there is an interaction between the three effects because of the plastic nature of the soil response.

Effective Stress Analysis

Page 48: Bearing Capacity ظرفيت باربري. Footing Shallow Foundations

•The formulae give the ultimate bearing capacity

•Significant deformations and large settlements may occur before general bearing failure occurs

•Local failure (yield) will occur at some depth beneath the footing at a load less than the ultimate collapse load

•The zone of plastic (yielding) soil will then spread as the load is increased. Only when the failure zone extends to the surface will a failure mechanism exist.

•A minimum load factor of 3 against ultimate failure is usually adopted to keep settlements within acceptable bounds, and to avoid problems with local failure.

Effective Stress Analysis

Page 49: Bearing Capacity ظرفيت باربري. Footing Shallow Foundations

Example

D = 2m

B = 5mQ

Page 50: Bearing Capacity ظرفيت باربري. Footing Shallow Foundations

Example

D = 2m

B = 5mQ

Determine short term and long term ultimate capacity given

Page 51: Bearing Capacity ظرفيت باربري. Footing Shallow Foundations

Example

qs

Q=q f B

Equivalent surface footing

Page 52: Bearing Capacity ظرفيت باربري. Footing Shallow Foundations

Example

qs

Q=q f B

Equivalent surface footing

Short term - Undrained (total stress) analysis

Page 53: Bearing Capacity ظرفيت باربري. Footing Shallow Foundations

Example

qs

Q=q f B

Equivalent surface footing

Short term - Undrained (total stress) analysis

Position of water table not important - soil must be saturated

Page 54: Bearing Capacity ظرفيت باربري. Footing Shallow Foundations

Example

qs

Q=q f B

Equivalent surface footing

Short term - Undrained (total stress) analysis

Position of water table not important - soil must be saturated

Page 55: Bearing Capacity ظرفيت باربري. Footing Shallow Foundations

Example

BEARING CAPACITY FACTORS [After Terzaghi and Peck (1948)]

60 50 40 30 20 10 0 20 40 60 80

N and N

0

10

20

30

40

(deg

rees

)

q c N

NN q

B

Da

bc

d

q= D

Q f

ff

Bearing capacity of a shallow foundation

ULTIMATE BEARING CAPACITY OF CLAY ( = 0 only) (After A.W. Skempton)

0 1 2 3 4 5

D/B

5

6

7

8

9

Nc

5.14

B

D

N (for rectangle)

= (0.84+0.16 ) N (square)

L= Length of footing

BL c

q = cNcult

q = B N + cN + D N continuous footing12f c f q

q = 0.4 BN + 1.3cN + D N squaref c f q

q = 0.6 RN + 1.3cN + D N circularf c f q

q = cN + Df c

c

Nc

BEARING CAPACITY THEORIES OF TERZAGHI AND SKEMPTON

u = 0 Nq = 1, N = 0 and Nc = 5.14

Page 56: Bearing Capacity ظرفيت باربري. Footing Shallow Foundations

Example

Short term capacity

q q NB

N c Nf s q c

2

Page 57: Bearing Capacity ظرفيت باربري. Footing Shallow Foundations

Example

Short term capacity

q q NB

N c Nf s q c

2

q f = 30 1 + 0 + 25 5.14 = 158.5 kPa (Bearing capacity)

Page 58: Bearing Capacity ظرفيت باربري. Footing Shallow Foundations

Example

Short term capacity

q q NB

N c Nf s q c

2

q f = 30 1 + 0 + 25 5.14 = 158.5 kPa (Bearing capacity)

Q = q f B = 158.5 5 = 792.5 kN/m (Bearing Force)

Page 59: Bearing Capacity ظرفيت باربري. Footing Shallow Foundations

Example

Long term capacity

Effective stress (fully drained) analysis

Page 60: Bearing Capacity ظرفيت باربري. Footing Shallow Foundations

Example

Long term capacity

Effective stress (fully drained) analysis

Page 61: Bearing Capacity ظرفيت باربري. Footing Shallow Foundations

Example

Long term capacity

Effective stress (fully drained) analysis

Page 62: Bearing Capacity ظرفيت باربري. Footing Shallow Foundations

Example

Long term capacity

Effective stress (fully drained) analysis

Page 63: Bearing Capacity ظرفيت باربري. Footing Shallow Foundations

Example

Long term capacity

Effective stress (fully drained) analysis

Page 64: Bearing Capacity ظرفيت باربري. Footing Shallow Foundations

Example

BEARING CAPACITY FACTORS [After Terzaghi and Peck (1948)]

60 50 40 30 20 10 0 20 40 60 80

N and N

0

10

20

30

40

(deg

rees

)

q c N

NN q

B

Da

bc

d

q= D

Q f

ff

Bearing capacity of a shallow foundation

ULTIMATE BEARING CAPACITY OF CLAY ( = 0 only) (After A.W. Skempton)

0 1 2 3 4 5

D/B

5

6

7

8

9

Nc

5.14

B

D

N (for rectangle)

= (0.84+0.16 ) N (square)

L= Length of footing

BL c

q = cNcult

q = B N + cN + D N continuous footing12f c f q

q = 0.4 BN + 1.3cN + D N squaref c f q

q = 0.6 RN + 1.3cN + D N circularf c f q

q = cN + Df c

c

Nc

BEARING CAPACITY THEORIES OF TERZAGHI AND SKEMPTON

’ = 25 Nq = 13, N = 10 and Nc = 24.5

Page 65: Bearing Capacity ظرفيت باربري. Footing Shallow Foundations

Example

Long term capacity

Page 66: Bearing Capacity ظرفيت باربري. Footing Shallow Foundations

Example

Long term capacity

Page 67: Bearing Capacity ظرفيت باربري. Footing Shallow Foundations

Example

Long term capacity

Page 68: Bearing Capacity ظرفيت باربري. Footing Shallow Foundations

Total Stress Analysis u = 0

f c u sq = N c + q

Page 69: Bearing Capacity ظرفيت باربري. Footing Shallow Foundations

Total Stress Analysis u = 0

f c u sq = N c + q

BEARING CAPACITY FACTORS [After Terzaghi and Peck (1948)]

60 50 40 30 20 10 0 20 40 60 80

N and N

0

10

20

30

40

(deg

rees

)

q c N

NN q

B

Da

bc

d

q= D

Q f

ff

Bearing capacity of a shallow foundation

ULTIMATE BEARING CAPACITY OF CLAY ( = 0 only) (After A.W. Skempton)

0 1 2 3 4 5

D/B

5

6

7

8

9

Nc

5.14

B

D

N (for rectangle)

= (0.84+0.16 ) N (square)

L= Length of footing

BL c

q = cNcult

q = B N + cN + D N continuous footing12f c f q

q = 0.4 BN + 1.3cN + D N squaref c f q

q = 0.6 RN + 1.3cN + D N circularf c f q

q = cN + Df c

c

Nc

BEARING CAPACITY THEORIES OF TERZAGHI AND SKEMPTON

Page 70: Bearing Capacity ظرفيت باربري. Footing Shallow Foundations

Bottom heave into excavations

D

B

heave

Page 71: Bearing Capacity ظرفيت باربري. Footing Shallow Foundations

Bottom heave into excavations

D

Page 72: Bearing Capacity ظرفيت باربري. Footing Shallow Foundations

Bottom heave into excavations

D

Page 73: Bearing Capacity ظرفيت باربري. Footing Shallow Foundations

Bottom heave into excavations

D

Page 74: Bearing Capacity ظرفيت باربري. Footing Shallow Foundations

Bottom heave into excavations

D