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!