Current U.S. Practice for LRFD Design of Drilled Shafts

Dan Brown, P.E.

Dan Brown and Associates

Major Factors Favoring Selection/Use of Drilled Shafts • Magnitude of loads

• Presence of strong bearing stratum at suitable depth

• Urban / Environmental (e.g., avoidance of pile driving noise & vibration)

• Elimination of footing (e.g., top down construction, cofferdams, congested area)

• Seismic or other high lateral demands

Trends • Larger diameters and depths: up to 13ft

(4m) dia and 260ft (80m) deep

• Greater demands for flexure, including considerations of seismic or other extreme event loads

• Greater acceptance of slurry or wet-hole techniques

• More congested sites, challenging applications

• Increased use of load testing and integrity testing

• Applications other than foundations; e.g., secant or tangent walls, cutoff walls

Axial Resistance – AASHTO (LRFD)

• Computed static side & base resistance from FHWA & State DOT guidelines

• Strength limit state, serviceability limit state

• Resistance factor increase for site-specific load testing (0.7 max for strength limit)

• 20% reduction in axial resistance for monoshaft foundation on single column pier

• Resistance factor of 1.0 for extreme event loading or conditions (seismic, collision, ice, extreme scour)

vessel PS

Mean Water

Level

Concept of Limit State A condition for which some component of the structure does not fulfill its design function

Can be defined in terms of:

• strength: for example, bearing capacity failure, structural yield in flexure

• serviceability: e.g., excessive settlement

• or in terms of strength or serviceability but for an extreme event, e.g., earthquake

LRFD Design Equation

iiiii RQ

ηi = load modifier for load component i

i = load factor for force component i

Qi = nominal value of force component i

i = resistance factor for resistance component i

Ri = nominal value of resistance component i

Notations

• (phi) is used for the LRFD resistance factor;

not to be confused with f (phi) used for the soil

friction angle

• (gamma) is used for both soil unit weight and

LRFD load factor

Load factors are subscripted to differentiate load

source, e.g., p = permanent load, L = live load

LRFD: The Basic Idea

Frequency of Occurrence

Magnitude of Force Effect or Resistance

Force

Resistance

LRFD: The Basic Idea (Cont’d)

QN

Q RN

RN

X Load

factors, X

Resistance

factors,

Nominal (unfactored) force effects (loads)

QN

Factored force effects

QN

Nominal (unfactored) resistances

RN

Factored resistances

RN

<

Resistance Factor: What Does it Mean?

• Resistance Factor: a multiplier used to reduce the nominal (calculated) resistance to achieve a design that is safe

• Safe: the probability that force effects will exceed resistance is sufficiently low

• Sufficiently low: 1 : 1,000 typical varies with limit state, consequences of failure, other factors

Terminology

Acceptable terms

• Nominal Resistance

• Nominal base resistance

• Factored resistance

• Displacement at service limit

• Factored force effects

• Extreme event conditions

Avoid these!

• Allowable load

• Capacity

• Design loads

• Ultimate capacity

AASHTO Limit States for Bridge Design AASHTO LIMIT STATES FOR BRIDGE DESIGN

Limit State Type Case Load Combination

Strength

I Normal vehicular use of the bridge without wind

II Use of the bridge by Owner-specified special vehicles, evaluation permit

vehicles, or both, without wind

III Bridge exposed to wind velocity exceeding 55 mph

IV Very high dead load to live load force effect ratios

V Normal vehicular use of the bridge with wind of 55 mph

Extreme Event I Load combination including earthquake

II Ice load, collision by vessels and vehicles, and certain hydraulic events with a

reduced live load other than that which is part of the vehicular collision load, CT

Service

I Normal operational use of the bridge with a 55 mph wind and all loads taken at

their nominal values

II Intended to control yielding of steel structures and slip of slip-critical

connections due to vehicular live load

III Longitudinal analysis relating to tension in prestressed concrete superstructures

with the objective of crack control and to principal tension in the webs of

segmental concrete girders

IV Tension in prestressed concrete columns with the objective of crack control

Fatigue Repetitive gravitational vehicular live load and dynamic responses under the

effects of a single design truck

AASHTO Load Combinations and Load Factors

(AFTER AASHTO 2007, TABLE 3.4.1-1) Use one of these at a time Load

Combination

Limit State PL LL WA WS WL FR TCS TG SE EQ IC CT CV

Strength I p 1.75 1.00 - - 1.00 0.50/1.20 TG SE - - - -

Strength II p 1.35 1.00 - - 1.00 0.50/1.20 TG SE - - - -

Strength III p - 1.00 1.40 - 1.00 0.50/1.20 TG SE - - - -

Strength IV p - 1.00 - - 1.00 0.50/1.20 - - - - - -

Strength V p 1.35 1.00 0.40 1.00 1.00 0.50/1.20 TG SE - - - -

Extreme Event I p EQ 1.00 - - 1.00 - - - 1.00 - - -

Extreme Event II p 0.50 1.00 - - 1.00 - - - - 1.00 1.00 1.00

Service I 1.00 1.00 1.00 0.30 1.00 1.00 1.00/1.20 TG SE - - - -

Service II 1.00 1.30 1.00 - - 1.00 1.00/1.20 - - - - - -

Service III 1.00 0.80 1.00 - - 1.00 1.00/1.20 TG SE - - - -

Service IV 1.00 - 1.00 0.70 - 1.00 1.00/1.20 - 1.00 - - - -

Fatigue - 0.75 - - - - - - - - - - -

PL permanent load WL wind on live load EQ earthquake

LL live load FR friction IC ice load

WA water load and stream pressure TG temperature gradient CT vehicular collision force

WS wind load on structure SE settlement CV vessel collision force

TCS uniform temperature, creep, and shrinkage

Structural Analysis of Bridge Used to Establish Foundation Force Effects

MR

VR

QR

M

V

Q

Reactions at fixed-end column supports obtained from structural analysis model of superstructure are taken as axial, shear, and moment force effects applied to top of the foundation

Bridge subjected to load combination corresponding to one of the limit states in Table 10-2

Reactions at column-shaft

connection obtained from

structural analysis model of

superstructure are taken

as axial, shear, and

moment force effects

applied to top of foundation

Bridge subjected to load combination corresponding to one

of the limit states in Table 10-3

Strength Limit States for Drilled Shafts

• Lateral geotechnical resistance of soil and rock stratum, for single shafts and shaft groups

• Geotechnical axial resistance (compression and uplift), for single shafts and shaft groups

• Structural resistance of shafts, including checks for axial, lateral, and flexural resistances

• Resistance when scour or other unusual conditions occur

Service Limit States for Drilled Shafts

• Settlement (vertical deformation)

• Horizontal movements at the top of the foundation

• Rotations at the top of the foundation

• Settlement and horizontal movements under scour at the design flood

• Settlement due to downdrag

Design for Lateral Loading • Geotechnical Strength Limit State

• Pushover failure – minimum embedment

• Structural Strength Limit State • Yield in flexure

• Serviceability Limit State • Lateral Deformations

• Extreme Event Conditions • Strength at max scour, seismic

7-17 Moment (ft-kips)

P (

kip

s)

Nominal Resistance

Factored Resistance

Permissible

Design for Axial Loading

• Geotechnical Strength Limit State • Axial failure – plunging or 5% displacement

• Structural Strength Limit State

• Serviceability Limit State • Settlement

• Extreme Event Conditions • Strength at max scour, seismic

Interpretation of Axial Load Test Data

sand

rock

38’

23’

50’

Test Shaft

-2.5

-2.0

-1.5

-1.0

-0.5

0.0

0 1000 2000 3000

Load (kips)

Dis

pla

ce

me

nt

(in

ch

es

)

19-19

Interpretation of Strain Gauge Data

-2.0

-1.5

-1.0

-0.5

0.0

0 200 400 600 800 1000 1200

Load (kips)

To

e D

isp

lac

em

en

t

(in

ch

es

)

-2

-1.5

-1

-0.5

0

0 5 10 15 20

Side Shear (ksf)

Se

gm

en

t D

isp

lac

em

en

t

(in

ch

es

)

19-20

Resistance Factors for Drilled Shafts Limit State Component of Resistance Geomaterial

Equation, Method, or Chapter

Reference

Resistance

Factor,

Strength I through

Strength V

Geotechnical

Lateral Resistance

Overturning of individual elastic shaft;

head free to rotate All geomaterials

p-y method pushover analysis;

Ch. 12 0.67

Overturning of single row, retaining wall

or abutment; head free to rotate All geomaterials p-y pushover analysis 0.67

Pushover of elastic shaft within multiple-

row group, w/ moment connection to cap All geomaterials p-y pushover analysis 0.80

Strength I through

Strength V

Geotechnical Axial

Resistance

Side resistance in compression/uplift

Cohesionless soil or IGM Beta method 0.55 / 0.45

Cohesive soil Alpha method 0.45 / 0.35

Rock Eq. 13-35 0.55 / 0.45

Cohesive IGM Modified alpha method 0.60 / 0.50

Base resistance in compression

Cohesionless soil 1. N-value 0.50

Cohesive soil Bearing capacity eq. 0.40

Rock and Cohesive IGM 1. Eq. 13-22

2. CGS (1985)

0.55

0.50

Static compressive resistance from load

tests All geomaterials < 0.7

Static uplift resistance from load tests All geomaterials 0.60

Group block failure Cohesive soil 0.55

Group uplift resistance Cohesive and cohesionless soil 0.45

Strength I through

Strength V;

Structural

Resistance of R/C

Axial compression 0.75

Combined axial and flexure 0.75 to 0.90

Shear 0.90

Service I All cases, all geomaterials Ch. 13, Appendix B 1.00

Extreme Event I

and II

Axial geotechnical uplift resistance All geomaterials Methods cited above for Strength

Limit States 0.80

Geotechnical lateral resistance All geomaterials p-y method pushover analysis; Ch.

12 0.80

All other cases All geomaterials Methods cited above for Strength

Limit States 1.00

Table 10-5

Reference Manual

Resistance Factors: Redundancy

Resistance factor values in AASHTO and in

the Reference Manual are based on the

assumption that drilled shafts are used in

groups of 2 to 4 shafts

• φ-values decreased by 20% for single shaft

supporting a bridge pier

Agency-Specific Resistance Factors • For design equations not covered in AASHTO or in the

Reference Manual

• For specific geomaterials encountered locally or regionally

• For local construction practices

Agencies have the option, in fact are encouraged, to conduct in-house calibration studies to establish resistance factors for the cases above

Section 10.1.1.2 of Reference Manual

Transportation Research Circular No. E-C079

Summary

• LRFD base design approach is now well-established

• Basis for design includes rational approach for: • Serviceability

• Strength

• Extreme event conditions

• We need to use consistent terminology to avoid confusion and mistakes!

Thanks for Listening!