nchrp 24-31 lrfd design specifications for shallow ... on distribution of bridge foundation usage...

NCHRP Report 651

LRFD DESIGN AND CONSTRUCTION OF

SHALLOW FOUNDATIONS FOR HIGHWAY

STRUCTURES

Samuel G. Paikowsky, Mary C. Canniff, Kerstin Lesny,

Aloys Kisse, Shailendra Amatya, and Robert Muganga

Geosciences Testing & Research, Inc.

N. Chelmsford, MA USA

NCHRP 24-31 LRFD Design Specifications for Shallow

Foundations

TRB AFS30 Committee Meeting January 26, 2011

The lecture is based on

Geotechnical Engineering Research Laboratory

Dept. of Civil and Environmental Engineering

University of Massachusetts Lowell.

OBJECTIVES

NCHRP RESEARCH PROJECT 24-31

Develop and Calibrate Procedures and Modify AASHTO’s Section 10 (Foundations) Specifications for the Strength Limit State Design of Bridge Shallow Foundations.

For NCHRP Research Report 651, Google NCHRP 651

2

Task 1: Design & Construction Practices

Questionnaire - Establishing design methods,

construction practices, design cases, and loads

Developed and distributed to 161 State Highway

Officials, TRB Representatives, and State and

FHWA bridge engineers.

Obtained responses from 39 states and 1

Canadian Province

Previous relevant information was obtained via a

questionnaire circulated in 2004 for the research

project NCHRP 12-66 AASHTO LRFD

Specifications for the Serviceability in the Design

of Bridge Foundation

3

Design & Construction Practices - Questionnaire Foundation AlternativesResults on distribution of bridge foundation usage from our previous questionnaires conducted in 1999 and 2004, and the current questionnaire (over the past 3 years, 2004-2006):

shallow foundations driven piles drilled foundations

1999/2004 14%/17% 75%/62% 11%/21%

current 17% 59% 24%

The average use changes significantly across the country. The use of shallow foundations in the Northeast exceeds by far all other regions of the USA, ranging from 40% in NY, NJ and ME, to 67% in CT. Other “heavy users” are TN (63%), WA (30%), NV (25%) and ID (20%). In contrast, out of the 39 responding states, six states do not use shallow foundations for bridges at all, and additional eight states use shallow foundations in 5% or less of the highway bridge foundations.

In summary, 55.8% of the shallow foundations are built on rock(average of piers and abutments) with additional 16.8% on IGM, hence 72.6% of the foundations are build on rock or cemented soils and only 27.4% are built on soils of which 24.2% on granular soils and 3.2% on clay or silt.

4

TASK 2: DATABASES

UML-GTR ShalFound07 Database549 cases built in ACCESS platform, 415 cases are suitable for

ULS.

UML-GTR RockFound07 Capacity Database

122 Cases of load tests to failure including 61 rock sockets, 33

shallow foundations on rock surface, 28 shallow foundations

below surface

ShalFound07

Divided into vertical centric and eccentric, and inclined cases

RockFound07

All vertical centric, shallow and drilled shafts

5

Database – Overview

UML-GTR ShalFound07

Sand Gravel Cohesive Mix Others Germany Others

Plate load tests

B 1m346 46 -- 2 72 466 253 213

Small footings

1 < B 3m26 2 -- 4 1 33 -- 33

Large footings

3 < B 6m30 -- -- 1 -- 31 -- 31

Rafts & Mats

B > 6m13 -- -- 5 1 19 1 18

Total 415 48 0 12 74 549 254 295

Note:

“Mixed” are cases with alternating layers of sand or gravel and clay or silt

“Others” are cases with either unknown soil types or with other granular materials like loamy Scoria

1m 3.3ft

TotalPredominant Soil Type CountryFoundation

type

6

Large foundations are often not loaded to ULS failure (SLS controls)

TASK 3: BC Shallow Foundations on Soil - OUTLINE

1. BC of Shallow foundations

BC Factors

BC modification Factors

2. Determination of ULS from case histories ULS and Modes of Failure – Overview Modes of Failure

3. Failure (Ultimate Load) Criteria Minimum slope criteria (Vesić, 1963) Limited settlement criterion of 0.1B (Vesić, 1975) Log-log plot of load-settlement curve (DeBeer, 1967) Two-slope criterion Selection of failure criteria (representative values and minimum

slope) Examples in soil & rock

4. Uncertainty Evaluation – BC of Centric Vertically Loaded Footing on Granular Soils Database overview Calculated BC – missing soil parameters and equations used for BC

calculations

5. Calibration

6. Summary and Conclusions

7

Recommended Failure Criterion

Minimum Slope Failure Load Criterion, Vesic (1963)

Failure load interpreted were for 196 cases using each of the

proposed methods

“Representative Failure Load” defined as the mean value of all

the failure loads interpreted using each criterion

Mean of the ratio was 0.98 and

Failure Loads for most cases

could be interpreted using

Minimum Slope criterion – the

criterion was chosen as the

standard BC interpretation

method

8

Bias of Estimated BC

Cases with Vertical Centric Loading

Vertical Centric Loading

n = 173; mean bias = 1.59, COV = 0.291

Natural soil conditions

(f from SPT-N counts)

n = 14; no. of sites = 8

mean = 1.00

COV = 0.329

Controlled soil conditions

(Dr 35%)

n = 159; no. of sites = 7

mean = 1.64

COV = 0.267

B > 1.0m

n = 6

no. of sites = 3

mean = 1.01

COV = 0.228

0.1 < B 1.0m

n = 8

no. of sites = 7

mean = 0.99

COV = 0.407

B 0.1m

n = 138

no. of sites = 5

mean = 1.67

COV = 0.245

0.1 < B 1.0m

n = 21

no. of sites = 3

mean = 1.48

COV = 0.391

Figure 60 Summary of bias (measured over calculated BC) for vertical centric

loading cases (Database I); 0.1m = 3.94in; 1m = 3.28ft.

9



Figure 61. (a) Histogram and probability density functions of the bias and (b)

relationship between measured and calculated bearing capacity for all cases

of vertical centrically loaded shallow foundations.

0.2 0.6 1 1.4 1.8 2.2 2.6 3 3.4 3.8

Bias, qu,meas / qu,calc

0

10

20

30

40

Nu

mb

er o

f o

bse

rvat

ions

0

0.1

0.2

Fre

qu

ency

Vertical-centric loading

n = 173mean = 1.59

COV = 0.291

lognormal

distribution

normal

distribution

0.1 1 10 100Calcualted bearing capacity, qu,calc

(Vesic, 1975 and modified AASHTO)

(ksf)

0.1

1

10

100

Inte

rpre

ted

bea

ring c

apac

ity, q

u,m

eas

usi

ng

Min

imum

Slo

pe

crit

erio

n (

Ves

ic,

196

3)

(ksf

)

Vertical-centric loadingData (n = 173)

Data best fit line

No bias line

10




relationship between measured and calculated bearing capacity for vertical

centrically loaded shallow foundations on controlled soil conditions.

0.2 0.6 1 1.4 1.8 2.2 2.6 3 3.4 3.8


0

10

20

30

40

Nu

mb

er o

f o

bse

rvat

ions

0

0.1

0.2

0.3

Fre

qu

ency

Controlled soil conditions

n = 159mean = 1.64

COV = 0.267

lognormal

distribution

normal

distribution



(ksf)

0.1

1

10

100

Inte

rpre

ted

bea

ring c

apac

ity, q

u,m

eas

usi

ng

Min

imum

Slo

pe

crit

erio

n (

Ves

ic,

196

3)

(ksf

)

Controlled soil conditionsData (n = 159)

Data best fit line

No bias line

11




relationship between measured and calculated bearing capacity for vertical

centrically loaded shallow foundations on natural soil conditions.

0.2 0.6 1 1.4 1.8 2.2 2.6 3 3.4 3.8


0

1

2

3

4

5

6

Nu

mb

er o

f o

bse

rvat

ions

0

0.1

0.2

0.3

0.4

Fre

qu

ency

Natural soil conditions

n = 14

mean = 1.00

COV = 0.329

lognormal

distribution

normal

distribution

1 10 100Calcualted bearing capacity, qu,calc


(ksf)

1

10

100

Inte

rpre

ted

bea

ring c

apac

ity, q

u,m

eas

usi

ng

Min

imum

Slo

pe

crit

erio

n (

Ves

ic,

196

3)

(ksf

)

Natural soil conditionsData (n = 14)

Data best fit line

No bias line

12

Bias versus Footing Width

Figure 100. Variation of the bias in bearing resistance versus footing

size for cases under vertical-centric loadings: f 43 and f < 43.

0.01 0.1 1

Footing width, B (m)

0.5

1

1.5

2

2.5

3

3.5

Bia

s

0.1 1 10B (ft)

(5)

(34)

(4)

(90)

(5)

(2)

(1)(17)

(1)

(3)

(4)

(3)

(1)

(2)

Mean bias BC (n = 172) s.d.

(x) no. of cases in each interval

95% confidence interval for f (n = 135)

95% confidence interval for f (n = 37)

13

Uncertainty in N

Comparison of bearing capacity factor calculated based on test results;

N = qu / (0.5 B s) from 125 tests carried out in controlled soil conditions

(tests by Perau, 1995) and N proposed by Vesic (1973) in the range of soil

friction angle of 42 and 46

42 43 44 45 46

friction angle, f (deg)

10

100

1000q

u /

(0.5

B

s)

N from load tests; n = 125

N (Vesic, 1973)

N = exp(0.39f 11.546)

(R2 = 0.666)

14

Uncertainty in N

42 43 44 45 46

Friction Angle, f (deg)

0

0.5

1

1.5

2

2.5

3

N

= [

qu /

(0.5

B

s)

] /

NV

esic

load test data; n = 125

= exp(0.205f 8.655) (R2 = 0.351)

Figure 93. The ratio (N) between the back-calculated B.C. factor N

based on experimental data to that proposed by Vesić versus soil

friction angle.

15

Uncertainty in N

Figure 94. The ratio between measured and calculated bearing

capacity (bias ) compared to the bias in the B.C. factor N (N) versus

the soil’s friction angle for footings under vertical-centric loadings.

43 44 45 46

Friction Angle, f (deg)

0

0.5

1

1.5

2

2.5

3

Bia

s

Data BC bias (n = 131)

Bearing Capacity (BC) bias,

N bias,

16

Uncertainty in B.C.

Figure 103. Bearing resistance bias vs. average soil friction angle

(taken f 0.5) including 95% confidence interval for all cases under

vertical-centric loading.

30 32 34 36 38 40 42 44 46

Friction angle f (deg)

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

Bia

s

(2)

(90)

(30)

(14)(4)

(2)

(12)

(4)

(3)

(2)

(3)

(4)

(2)

Mean bias,BC (n = 172) 1 s.d.


BC = 0.308exp(0.0372f)

(R2=0.200)

95% confidence interval

17

Final Resistance Factors – Controlled Conditions

Table 66 Recommended resistance factors for shallow foundations on granular

soils placed under controlled conditions

Soil friction

angle f

Loading conditions

Vertical-centric or

-eccentricInclined-centric

Inclined-eccentric

Positive Negative

0° ° 0.500.40 0.40 0.70

° ° 0.60

° 9° 0.70 0.45 0.45 0.75

0° ° 0.75 0.500.50 0.80

° 0.80 0.55

Notes:

1) f determined by laboratory testing

2) compacted controlled fill or improved ground are assumed to extend below the base

of the footing to a distance to at least two (2.0) times the width of the foundation (B).

If the fill is less than 2B thick, but overlays a material equal or better in strength than

the fill itself, then the recommendation stands. If not, then the strength of the

weaker material within a distance of 2B below the footing; prevails.

3) The resistance factors were evaluated for a target reliability T = 3.0.

18

Final Resistance Factors – Natural Conditions

Table 67 Recommended resistance factors for shallow foundations on natural

deposited granular soil conditions

Notes:

1) f determined from Standard Penetration Test results

2) granular material is assumed to extend below the base of the footing at least two

(2.0) times the width of the foundation.

3) The resistance factors were evaluated for a target reliability T = 3.0

Soil friction

angle f

Loading conditions

Vertical-centric or


Inclined-eccentric

Positive Negative

0° ° 0.400.40

0.35 0.65

° ° 0.450.70

° 9° 0.500.40

0° ° 0.55 0.450.75

° 0.65 0.50 0.45

19

Intermediate Conclusions and Summary

It was found that for the footings of larger sizes (B>3m (9.9ft)),

the load tests were not carried out to the failure load

Biases for the tests in Natural Soil Condition and Controlled

Soil Conditions were analyzed separately

For the footing sizes in similar ranges (0.1m < B 1.0m), the

scatter of bias was larger for footings on/in natural soil

conditions

The majority of the relevant data refers to small size

foundations (B 3.3ft (1.0m)) on controlled compacted

material. Many of the highway shallow foundations on soils

are built on compacted materials and hence, the statistical

data of the uncertainty can be used for that purpose

There appears to be a trend of increase in bias with the

footing size within the range of footing sizes available for

testing (which seems to conform with the observation made

by Vesic (1969))

20

ULS of Inclined Loading

Figure 64. Loading convention and load paths used during

tests.

3b

1x

2F3M

1M

2M1F

2x

3F

2b

D

3x

g

f

B

1x

2F 3M

1M 2M1F

2x

3F

L

D

3x

(a) Loading convention

F1

F3

F1

F3

1,const.

increasing = const.

F1

M2

arctan e = const

(b) Radial load path (c) Step-like load path

F

Figure 4.7. Loading convention and load paths used during tests

21

ULS of Inclined Loading

Figure 65. Load–displacements curves for model tests

conducted by Montrasio (1994) with varying load inclination:

(a) vertical load vs. vertical displacement and (b) horizontal

load vs. horizontal displacement.

0 1 2 3 4

Vertical load, F1 , F10 (kN)

8

6

4

2

0

Ver

tica

l d

ispla

cem

ent, u

1 (

mm

)

0 0.2 0.4 0.6 0.8 1F1 (kips)

0.3

0.2

0.1

0

u1 (

in)

MoD2.1 = 3

MoD2.2 = 8

MoD2.3 = 14

MoA2.1 = 0F0

0 0.2 0.4 0.6 0.8 1 1.2

Horizontal load, F3 (kN)

6

4

2

0

Ho

rizo

nta

l d

ispla

cem

ent, u

3 (

mm

)0 0.05 0.1 0.15 0.2 0.25

F3 (kips)

0.2

0.1

0

u3 (

in)

MoD2.1 = 3

MoD2.2 = 8

MoD2.3 = 14

22

Figure 66. (a) Histogram and probability density functions of

the bias and (b) relationship between measured and calculated

bearing capacity for all cases of vertical eccentrically loaded

shallow foundations.

0.4 1.2 2 2.8 3.6


0

2

4

6

8

10

12

Nu

mb

er o

f o

bse

rvat

ions

0

0.05

0.1

0.15

0.2

0.25

Fre

qu

ency

Vertical-eccentric loading

n = 43mean = 1.83

COV = 0.351

lognormal

distribution

normal

distribution



(ksf)

0.1

1

10

100

1000

Inte

rpre

ted

bea

ring c

apac

ity, q

u,m

eas

usi

ng

Min

imum

Slo

pe

crit

erio

n (

Ves

ic,

196

3)

(ksf

)

Vertical-eccentric loadingData (n = 43)

Data best fit line

No bias line


Cases with Vertical-Eccentric Loading (using B)

23

Figure 105. Bearing resistance bias versus soil friction angle for

cases under vertical-eccentric loadings; seven cases for f = 35

(all from a single site) have been ignored for obtaining the

best fit line.

30 32 34 36 38 40 42 44 46


0.0

0.5

1.0

1.5

2.0

2.5

3.0

Bia

s

(7)

(6)

(4)

(2)

(9)

(4)

(11)

Mean bias, BC 1 s.d.


BC = 2.592´exp(-0.01124f) (R2=0.01)

95% confidence interval

n = 43


Cases with Vertical-Eccentric Loading

24

Figure 67. (a) Histogram and probability density functions of the

bias and (b) relationship between measured and calculated

bearing capacity for all cases of inclined centric loaded shallow

foundations.

0.2 0.6 1 1.4 1.8 2.2 2.6


0

4

8

12

Nu

mb

er o

f o

bse

rvat

ions

0

0.1

0.2

0.3

Fre

qu

ency

Inclined-centric loading

n = 39

mean = 1.43

COV = 0.295

lognormal

distributionnormal

distribution



(ksf)

0.1

1

10

100

Inte

rpre

ted

bea

ring c

apac

ity, q

u,m

eas

usi

ng

Min

imum

Slo

pe

crit

erio

n (

Ves

ic,

196

3)

(ksf

)

Inclined-centric loadingData (n = 39)

Data best fit line

No bias line


Cases with Inclined-Centric Loading

25



bearing capacity for all cases of inclined eccentrically loaded

shallow foundations.

1.2 1.8 2.4 3 3.6 4.2 4.8 5.4 6 6.6 7.2


0

1

2

3

4

5

6

7

8

9

Nu

mb

er o

f o

bse

rvat

ions

0

0.05

0.1

0.15

0.2

0.25

0.3

Fre

qu

ency

Inclined-eccentric loading

n = 29

mean = 2.43

COV = 0.508

lognormal

distribution

normal

distribution



(ksf)

0.1

1

10

100

Inte

rpre

ted

bea

ring c

apac

ity, q

u,m

eas

usi

ng

Min

imum

Slo

pe

crit

erio

n (

Ves

ic,

196

3)

(ksf

)

Inclined-eccentric loadingData (n = 29)

Data best fit line

No bias line


Cases with Inclined-Eccentric Loading

26

Loading Directions for Inclined-Eccentric Loadings

Figure 69. Loading directions for the case of inclined-eccentric

loadings: (a) along footing width and (b) along footing length

e

3

F

1

b

3

F

3

M2

F

1 F

3

+

+

e

3

F

1

b

3

F

3

M2

F

1 F

3

+

Moment acting in the same direction as the lateral loading – positive

eccentricity

Moment acting in direction opposite to the lateral loading – negative

eccentricity

b

3

b

3

(a) along footing width

e

2

F

1

b

2

F

2

M3

F

1

b

2

F

2

+

-

e

2

F

1

b

2

F

2

M3

F

1

b

2

F

2

+

+

Moment acting in the same direction as the lateral loading – positive

eccentricity

Moment acting in direction opposite to the lateral loading – negative

eccentricity

(b) along footing length

27



bearing capacity for all cases of inclined eccentrically loaded

shallow foundations under negative eccentricity.

1.2 1.8 2.4 3 3.6 4.2 4.8 5.4 6 6.6 7.2


0

1

2

3

Nu

mb

er o

f o

bse

rvat

ions

0

0.1

0.2

0.3

0.4

0.5

Fre

qu

ency


Negative eccentricity

n = 7

mean = 3.43

COV = 0.523

normal

distribution

lognormal

distribution

0.1 1 10Calcualted bearing capacity, qu,calc


(ksf)

0.1

1

10

Inte

rpre

ted

bea

ring c

apac

ity, q

u,m

eas

usi

ng

Min

imum

Slo

pe

crit

erio

n (

Ves

ic,

196

3)

(ksf

)


Negative eccentricityData (n = 7)

Data best fit line

No bias line


Cases with Inclined-Eccentric Loading

28

Final Resistance Factors – Natural Conditions

Table 67 Recommended resistance factors for shallow foundations on natural

deposited granular soil conditions

Notes:

1) f determined from Standard Penetration Test results

2) granular material is assumed to extend below the base of the footing at least two

(2.0) times the width of the foundation.

3) The resistance factors were evaluated for a target reliability T = 3.0

Soil friction

angle f

Loading conditions

Vertical-centric or


Inclined-eccentric

Positive Negative

0° ° 0.400.40

0.35 0.65

° ° 0.450.70

° 9° 0.500.40

0° ° 0.55 0.450.75

° 0.65 0.50 0.45

29

Developed as a part of Project NCHRP 12-66

Bias = measured load / calculated load for a given

settlement

For reliability index = 1.28 (pf = 10%), and load

factors taken as unity

Bias of LL = 1.15, COVQL = 0.2

Bias of DL = 1.05, COVQD = 0.1

Method Range of Settlement

(inch)

Resistance Factor

Efficiency Factor

/

0.00 < 1.00 0.85 0.34

1.00 < 1.50 0.80 0.48 AASHTO

1.50 < 3.00 0.60 0.48

Conceptual Design – Influence of Serviceability

’s based on Serviceability Limit States

30

Conceptual Design – Granular Soils

Example 2 NCHRP Report 651: Known Load and

Settlement

Central Pier of a

bridge in Billerica

(Rangeway Rd over

Rte.3) (B-12-025)

Design (factored)

load is 3688.3kips

for ultimate limit

state and 2750kips

for service limit state

(unfactored)

Allowable settlement

1.5inches

31


Factored Resistances (ksf)

32

2 4 6 8 10 12 14 16 18 20 22

Effective footing width, B (ft)

0

1000

2000

3000

4000

5000

Fac

tore

d u

ltim

ate

lim

it s

tate

an

d

unfa

ctore

d s

ervic

e li

mit

sta

te (

kip

s)

1 2 3 4 5 6

Effective footing width, B (m)

0

5

10

15

20

Fac

tore

d u

ltim

ate

lim

it s

tate

an

d

un

fact

ore

d s

ervic

e li

mit

sta

te (

MN

)

2 4 6 8 10 12 14 16 18 20 22


0

5

10

15

20

25

Fac

tore

d u

ltim

ate

lim

it s

tate

an

d

unfa

ctore

d s

ervic

e li

mit

sta

te (

ksf

)

1 2 3 4 5 6


0

0.25

0.5

0.75

1

Fac

tore

d u

ltim

ate

lim

it s

tate

an

d

un

fact

ore

d s

erv

ice

lim

it s

tate

(M

Pa)

Strength LS, C2 load 00


Strength LS 0AASHTO, 2007)

Service LS AASHTO (2007)

Service LS Schmertmann (1978)

Service LS Hough (1959)

Service I loading

Strength I, C2 loading

Strength I, C7 loading2 4 6 8 10 12 14 16 18 20 22


0

1000

2000

3000

4000

5000

Fac

tore

d u

ltim

ate

lim

it s

tate

an

d

unfa

ctore

d s

ervic

e li

mit

sta

te (

kip

s)

1 2 3 4 5 6


0

5

10

15

20

Fac

tore

d u

ltim

ate

lim

it s

tate

an

d

un

fact

ore

d s

ervic

e li

mit

sta

te (

MN

)

2 4 6 8 10 12 14 16 18 20 22


0

5

10

15

20

25

Fac

tore

d u

ltim

ate

lim

it s

tate

an

d

unfa

ctore

d s

ervic

e li

mit

sta

te (

ksf

)

1 2 3 4 5 6


0

0.25

0.5

0.75

1

Fac

tore

d u

ltim

ate

lim

it s

tate

an

d

un

fact

ore

d s

erv

ice

lim

it s

tate

(M

Pa)







Service I loading



Figure H-6 Variation of factored bearing resistance for Strength-I and

unfactored resistance for Service-I limit state with effective footing width for

Example 2 (NCHRP Report 651)


Factored Resistances (kips)

Strength Limit State

loading

3688kips (phi=0.45)

B = 8.9ft (B’=7.9ft+2x0.5)

Service Limit state of

2750kips – B=4.5ft

(B’=3.5+2x0.5)

33

2 4 6 8 10 12 14 16 18 20 22


0

1000

2000

3000

4000

5000

Fac

tore

d u

ltim

ate

lim

it s

tate

an

d

unfa

ctore

d s

ervic

e li

mit

sta

te (

kip

s)

1 2 3 4 5 6


0

5

10

15

20

Fac

tore

d u

ltim

ate

lim

it s

tate

an

d

un

fact

ore

d s

ervic

e li

mit

sta

te (

MN

)

2 4 6 8 10 12 14 16 18 20 22


0

5

10

15

20

25

Fac

tore

d u

ltim

ate

lim

it s

tate

an

d

unfa

ctore

d s

ervic

e li

mit

sta

te (

ksf

)

1 2 3 4 5 6


0

0.25

0.5

0.75

1

Fac

tore

d u

ltim

ate

lim

it s

tate

an

d

un

fact

ore

d s

erv

ice

lim

it s

tate

(M

Pa)







Service I loading



Figure H-6 cont. Variation of factored bearing resistance for Strength-I and

unfactored resistance for Service-I limit state with effective footing width for

Example 2 (NCHRP Report 651)

2 4 6 8 10 12 14 16 18 20 22


0

1000

2000

3000

4000

5000

Fac

tore

d u

ltim

ate

lim

it s

tate

an

d

unfa

ctore

d s

ervic

e li

mit

sta

te (

kip

s)

1 2 3 4 5 6


0

5

10

15

20

Fac

tore

d u

ltim

ate

lim

it s

tate

an

d

un

fact

ore

d s

ervic

e li

mit

sta

te (

MN

)

2 4 6 8 10 12 14 16 18 20 22


0

5

10

15

20

25

Fac

tore

d u

ltim

ate

lim

it s

tate

an

d

unfa

ctore

d s

ervic

e li

mit

sta

te (

ksf

)

1 2 3 4 5 6


0

0.25

0.5

0.75

1

Fac

tore

d u

ltim

ate

lim

it s

tate

an

d

un

fact

ore

d s

erv

ice

lim

it s

tate

(M

Pa)







Service I loading



Intermediate Conclusions

The Strength Limit State governs the footing

dimensions in this design example with a

requirement for B=8.9ft vs. B=4.5ft for the service

limit state

The bridge was designed with B=13.1ft most likely

due to the differences in design procedures

(especially settlement)

34

Task 3: BC Shallow Foundations on Rock - OUTLINE

1. Broad Objectives

2. Database UML/GTR RockFound07

3. Rock Classification and Properties

4. Methods of Analyses Selected for

Establishing the Uncertainty in B.C. of

Foundations on Rock

5. Calibration – evaluation of resistance

factors

6. Summary and Conclusions

35

2. DATABASE UML/GTR RockFound 07

Comprised of 122 foundation case histories of load tests in/on rock and IGM’s.

The database has 61 footings cases (28 cases D>0, 33 cases D=0) and 61 rock socket cases for which the base behavior (load and displacement) under loading was monitored.

89 of the 122 cases were used for the uncertainty determination of the settlement of foundations on rock.

36

Hirany and Kulhawy (1988)

proposed the L1-L2 method

for interpreting the "failure"

load or "ultimate" capacity

of foundations from load-

displacement curves.

Hirany and Kulhawy (1988) Failure criterion

The unique peak or

asymptote value in the

curves is taken as the

measured or interpreted

capacity (QL2=qL2).

For 79 cases qL2 could be

evaluated, 43 cases are

based on reported failure

load.

37

Using the limit-equilibrium approach, Carter and

Kulhawy (1988) developed a lower bound to the B.C. for

strip and circular footings on jointed rock masses

presented below.

uult qsmq (2)

Carter and Kulhawy (1988) - B.C. of Foundations on Rock

38

Relationship between Carter and Kulhawy (1988) calculated bearing

capacity (qult) using two variations (equations 82a and 82b) and the

interpreted bearing capacity (qL2).


39

0.01 0.1 1 10 100 1000 10000 100000

Carter and Kulhawy (1988) Bearing Capacity qult (ksf)

1

10

100

1000

10000

100000

Inte

rpret

ed F

ou

nd

ati

on

Cap

aci

ty q

L2 (

ksf

)

58 Footings cases

61 Rock Socket cases

119 All cases withrevised equation

qL2 = 16.14 qult)0.619

(n = 119; R2 = 0.921)

qL2 = 36.51 qult)0.600 (Revised)

(n = 119; R2 = 0.917)

qL2 = qult

Table 69 Calibrated resistance factors for different datasets of resistance bias

obtained using Carter and Kulhawy’s (1988) method


40

Dataset No. of casesBias Resistance factor (T = 3)

Mean COV MCS Recommended

All cases 119 8.00 1.240 0.372 0.35

RMR 85 23 2.93 0.651 0.535 0.50

65 RMR < 85 57 3.78 0.463 1.149 1.00

44 RMR < 65 17 8.83 0.651 1.612 1.00

3 RMR < 44 22 23.62 0.574 5.295 1.00

The lower bound is represented by the following Equation:

1Nqquult

2

45tanN 2

in which

Goodman (1989) developed the B.C.

Equation 5 for footings resting on

orthogonal vertical joints each

spaced distance s in which lateral

stress transfer is nil.

1B

SN

1N

1qq

N1N

uult

(3)

(4)

(5)

Goodman (1989) - B.C. of Foundations on Rock

41

Summary of the statistics for the Ratio of Measured to Calculated

B.C. using Goodman’s (1989) Method

Cases nNo. of

Sites

Mean of

Bias

m

Standard

Deviation

s

COV

All Foundations 119 78 1.35 0.72 0.535

All rock sockets 61 49 1.52 0.82 0.541

All footings 58 29 1.23 0.66 0.539

Sub-categorization suggests that if more details of rock

measurements are available, the uncertainty is reduced.

1. 34 Rock Socket cases with measured discontinuity

spacing had a COVl = 0.48.

2. 8 Rock Socket cases with measured discontinuity

spacing and friction angle had a COVl = 0.18.


42

Figure 78. Relationship between Goodman’s (1989) calculated bearing capacity

(qult) and the interpreted bearing capacity (qL2).


43

1 10 100 1000 10000 100000

Goodman (1989) Bearing Capacity qult (ksf)

1

10

100

1000

10000

100000

Inte

rpret

ed

Fou

nd

ati

on

Cap

acit

y q

L2 (

ksf

)

58 Footings cases

61 Rock Socket cases

qL2 = 2.16 qult)0.868

(n = 119; R2 = 0.897)

qL2 = qult


44

0 0.6 1.2 1.8 2.4 3 3.6 4.2 4.8


0

10

20

30

40

Nu

mb

er

of

observ

ati

ons

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

Fre

qu

ency

119 Rock-sockets and Footing cases

Goodman (1989)

mean = 1.35

COV = 0.535

lognormal

distribution

normal

distribution

0 0.4 0.8 1.2 1.6 2 2.4 2.8 3.2


0

2

4

6

8

10

12

Nu

mb

er o

f o

bse

rvat

ions

0

0.1

0.2

0.3

0.4

0.5

0.6

Fre

qu

ency

20 Foundation cases on Fractured Rocks

Goodman (1989)

mean = 1.24

COV = 0.276

lognormal

distribution

normal

distribution

Figure 79. Distribution of the ratio of the

interpreted bearing capacity (qL2) to the

bearing capacity (qult) calculated using

Goodman’s (1989) method for the rock

sockets and footings in database UML-GTR

RockFound07.

Figure 80. Distribution of the ratio of the

interpreted bearing capacity (qL2) to the

bearing capacity (qult) calculated using

Goodman’s (1989) method for foundations

on fractured rock in database UML-GTR

RockFound07


45

-4

-2

0

2

4

Sta

nd

ard

norm

al

qu

an

tile

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5

Bias

B.C. using Goodman (1989)All data

Total data (n = 119)

Normal distribution

Lognormal distribution

= 1.35

COV = 0.535

Figure 113. Comparison of the unfiltered bias for BC calculated using Goodman

(1989) method for all data and the theoretical normal and lognormal distributions.

Table 68 Calibrated resistance factors for different datasets of resistance

bias obtained using Goodman’s (1989) method


46

Dataset No. of casesBias Resistance factor (T = 3)

Mean COV MCS Recommended

All data 119 1.35 0.535 0.336 0.30

Measured friction angle f 98 1.41 0.541 0.346 0.35

Measured spacing s 83 1.43 0.461 0.437 0.40

Measured friction angle f and s 67 1.51 0.459 0.464 0.45

Calibration of Resistance Factors

47

Method of

AnalysisEquation Application

Efficiency Factor

/

(%)

Carter and

Kulhawy

(1988)

All 0.35 4.4

RMR 85 0.50 17.1

65 RMR < 85

1.00

26.5

44 RMR < 65 11.3

3 RMR < 44 4.2

Goodman

(1989)

For fractured rocks:

For non-fractured rocks:

All 0.30 22.2

Measured f 0.35 24.8

Measured s 0.40 28.0

Measured s and f 0.45 29.8

ult uq q m s

1ult uq q N

( 1)1

11

N N

ult u

sq q N

N B

Table 70 Recommended resistance factors for foundations in/on

rock based on T = 3.0 (pf = 0.135%)

Uncertainty in B.C.

Figure 104. Recommended resistance factors for soil friction angles (taken f 0.5) between 30 and

46, with comparisons to 95% confidence interval and resistance factors obtained for the cases in the

database; the bubble size represents the number of data cases in each subset.

30 32 34 36 38 40 42 44 46


0.0

0.2

0.4

0.6

0.8

1.0

Res

ista

nce

fact

or,

0.0

0.5

1.0

1.5

2.0

2.5

3.0

Bia

s

(2)(90)

(30)

(14)(4)

(2)

(12)

(4)

(3)

(2)(3)

(4)

(2)

95% confidence interval for

Resistance factor based on database(x) no. of cases in each interval

Recommended f for Controlled soil conditions

Recommended f for Natural soil conditions

n = 172

49

Table 38 Summary of the statistics for the ratio of measured (qL2) to calculated

bearing capacity (qult) of rock sockets and footings on rock using Carter and

Kulhawy (1988) method


50

Cases nNo. of

Sitesm s COV

All rock sockets 61 49 4.29 3.08 0.716

All rock sockets on fractured rock 11 6 5.26 1.54 0.294

All rock sockets on non-fractured rock 50 43 4.08 3.29 0.807

Rock sockets on non-fractured rock with measured discontinuity

spacing (s')34 14 3.95 3.75 0.949

Rock sockets on non-fractured rock with s' based on AASHTO

(2007)16 13 4.36 2.09 0.480

All footings 58 29 11.90 12.794 1.075

All footings on fractured rock 9 3 2.58 2.54 0.985

All footings on non-fractured rock 49 26 13.62 13.19 0.969

Footings on non-fractured rock with measured discontinuity

spacing (s')29 11 15.55 14.08 0.905

Footings on non-fractured rock with s' based on AASHTO

(2007)20 11 10.81 11.56 1.069

n = number of case histories m = mean of biases s = standard deviation

COV = coefficient of variation Calculated capacity based on equation (82a)

Table 40 Summary of the statistics for the ratio of measured (qL2) to

calculated bearing capacity (qult) of rock sockets and footings on rock

using Goodman (1989) method


51

Cases nNo. of

Sitesm s COV

All 119 78 1.35 0.72 0.535

Measured discontinuity spacing (s') and friction angle (f) 67 43 1.51 0.69 0.459

Measured discontinuity spacing (s') 83 48 1.43 0.66 0.461

Measured friction angle (f) 98 71 1.41 0.76 0.541

Fractured 20 9 1.24 0.34 0.276

Fractured with measured friction angle (f) 12 7 1.33 0.25 0.189

Non-fractured 99 60 1.37 0.77 0.565

Non-fractured with measured s' and measured f 55 37 1.55 0.75 0.485

Non-fractured with measured discontinuity spacing (s') 63 39 1.49 0.72 0.485

Non-fractured with measured friction angle (f) 86 64 1.42 0.81 0.569

Spacing s' and f, both based on AASHTO (2007) 5 3 0.89 0.33 0.368

Discontinuity spacing (s') based on AASHTO (2007) 36 21 1.16 0.83 0.712

Friction angle (f) based on AASHTO (2007) 21 7 1.06 0.37 0.346n = number of case histories m = mean of biases s = standard deviation COV = coefficient of

variation

nchrp 24-31 lrfd design specifications for shallow ... on distribution of bridge foundation usage...

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