Bridge Design Practice 11.

1 • October 2022

CHAPTER 11.1 ABUTMENTS

11.1.1 INTRODUCTION .................................................................................................. 11.1-3
11.1.2 TYPES OF ABUTMENTS .................................................................................. 11.1-3
11.1.2.1 Open-End Abutments ............................................................................................. 11.1-3
11.1.2.2 Closed-End Abutments .......................................................................................... 11.1-3
11.1.3 LOADS AND LOAD COMBINATIONS ............................................................. 11.1-5
11.1.3.1 Dead Load (DCsup, DCsub, DW)............................................................................ 11.1-6
11.1.3.2 Live Load (LLHL93, LLPermit, LS) ............................................................................. 11.1-7
11.1.3.3 Horizontal Loads from Superstructure ............................................................... 11.1-8
11.1.3.4 Earth Pressure Components (EH, EV, ESH, ESV) ......................................... 11.1-8
11.1.3.5 Seismic Effects ......................................................................................................... 11.1-8
11.1.3.6 Construction Load Cases ...................................................................................... 11.1-9
11.1.4 STRUCTURAL COMPONENT DESIGN CONSIDERATION ......................... 11.1-9
11.1.5 FOUNDATION DESIGN CONSIDERATION .................................................. 11.1-10
11.1.5.1 Size Spread Footing.............................................................................................. 11.1-10
11.1.5.2 Determine Pile Tip Elevations ............................................................................ 11.1-10
11.1.5.3 Design Piles for Shear .......................................................................................... 11.1-10
11.1.5.4 Design Piles for Tension ...................................................................................... 11.1-11
11.1.6 DESIGN EXAMPLE .......................................................................................... 11.1-12
11.1.6.1 Abutment Data ........................................................................................................ 11.1-12
11.1.6.2 Design Requirements ........................................................................................... 11.1-15
11.1.6.3 Calculate Loads Transferred from Superstructure to Abutment .............. 11.1-16
11.1.6.4 Perform Live Load Analysis ................................................................................ 11.1-18
11.1.6.5 Calculate Load Combinations ............................................................................ 11.1-21
11.1.6.6 Design Backwall ..................................................................................................... 11.1-25
11.1.6.7 Design Stem Wall .................................................................................................. 11.1-30
11.1.6.8 Design Pile Foundation ........................................................................................ 11.1-35
11.1.6.9 Design Spread Footing......................................................................................... 11.1-41
NOTATION .................................................................................................................... 11.1-48
REFERENCES .............................................................................................................. 11.1-52

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 Bridge Design Practice 11.1 • October 2022

11.1.1 INTRODUCTION
Abutments are the substructure components at the ends of a bridge used to transfer the
loads from the superstructure to foundations, support approach slabs, and retain the
approach embankment. In the first part of this chapter, common types of abutments and
basic aspects of abutment design according to AASHTO LRFD Bridge Design
Specifications, 8th Edition with California Amendments, referred to herein as AASHTO-
CA BDS-8 (AASHTO, 2017; Caltrans, 2019a) are discussed. Subsequently, a design
example of the short seat (non-integral) abutment is presented to illustrate the typical
design procedure.

11.1.2 TYPES OF ABUTMENTS

The most common types of abutments used for highway bridges are shown in Figure
11.1.2-1. In general, abutments can be classified as open-end and closed-end. The
selection of an abutment type depends on the requirements for structural connections to
the superstructure, the superstructure’s horizontal movements, drainage, roadway
approach, and earthquake effects.

11.1.2.1 Open-End Abutments

As shown in Figure 11.1.2-1 (a), open-end abutments are constructed with a front slope
that allows an easier inspection and provides the room for future widening of the roadway
or waterway. They include diaphragm and short-seat abutments, also commonly referred
to as “integral” and “non-integral” abutments, respectively. Open-end abutments are the
most frequently used abutments for girder bridges and are usually the most economical,
adaptable, and attractive. The basic structural difference between the two types is that
seat abutments permit the superstructure to move independently from the abutment,
while the diaphragm abutments do not. Figure 11.1.2-2 shows the structural components
of a short-seat abutment.

11.1.2.2 Closed-End Abutments

As shown in Figure 11.1.2-1 (b) and (c), closed-end abutments are constructed close to
the edge of the roadway or waterway without a front embankment. They include high
cantilever, strutted, rigid frame, bin, and closure abutments. These are less commonly
used but suitable for bridge widening of the same kind, unusual sites, or tightly
constrained urban locations. Rigid frame abutments are generally utilized with tunnel-type
single-span connectors and overhead structures which permit passage through a
roadway embankment. Because the structural supports are adjacent to the traffic or the
waterway, these have a high initial cost and present a closed appearance to the
approaching traffic.

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 Bridge Design Practice 11.1 • October 2022

Diaphragm Seat

(a) Open-End abutments

Cantilever Strutted Rigid Frame

(b) Closed-End Backfilled Abutments

Bin Closure

(c) Closed-End Cellular Abutments

Figure 11.1.2-1 Typical Types of Abutments

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 Bridge Design Practice 11.1 • October 2022

The general detailing of abutments is covered in Bridge Design Details (BDD) Chapter 6.

wingwall

shear key

backwall

footing

stem

Figure 11.1.2-2 Structural Components of Short-Seat (Non-integral) Abutment

11.1.3 LOADS AND LOAD COMBINATIONS

The load factors and load combinations applicable to the abutment design are given in
Tables 11.1.3-1 and 11.1.3-2 (Tables 3.4.1-1 and 3.4.5.1-1 of AASHTO-CA BDS-8). The
construction load combinations have been added to carry Caltrans traditional working
stress design practice, where abutments are also checked during temporary construction
conditions. Construction load combinations, including Construction-I and Construction-II
cases according to Article 3.4.1 (AASHTO-CA BDS-8), are shown in Table 11.1.3-2.

Furthermore, sacrificial components of abutments such as backwalls and shear keys shall
be designed in accordance with SDC and AASHTO-CA BDS-8 requirements. Refer to
Article 3.4.5.2 for height limitations associated with this provision. The dynamic allowance
(IM) of the live load is disregarded for non-integral abutments refer to Article 3.6.2.1
(AASHTO-CA BDS-8).

Table 11.1.3-1 Service Limit State Load Factors for Abutments

Combination DCSup. DCSub. DD, EH, EV, LLHL93, IM, LLPermit, WA WS WL TU PS,
DW ESH ESV CE, BR, IM, CE CR,
PL, LS SH
Service-I 1.0 1.0 1.0 1.0 1.0 1.0 0 1.0 0.3 1.0 1.0 1.0

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Table 11.1.3-2 Strength and Construction Load Factors for Abutments

Combination DCSup. DCSub. DD DW EH LLHL93 LLPermit WA WS WL TU PS
ESH IM IM CR
EV CE CE SH
ESV
BR
PL
LS
Strength I γp γp γp γp γp 1.75 0 1.00 0 0 1.00 1.00
Strength II γp γp γp γp γp 0 1.35 1.00 0 0 1.00 1.00
Strength III γp γp γp γp γp 0 0 1.00 1.00 0 1.00 1.00
Strength V γp γp γp γp γp 1.35 0 1.00 1.00 1.00 1.00 1.00
Construction I 0 γp 0 0 γp 0 0 0 0 0 0 0
Construction II 1.25 1.25 0 1.50 0 0 0 0 0 0 1.00 1.00
Note: For γp values of abutments, refer to Table 11.1.3-2a.

Table 11.1.3-2a Load Factors for Permanent Loads, γp

Load Factor
Type of Load and Method Used to Calculate Downdrag
Maximum Minimum
DCSub: Dead Load of Structure Components and Nonstructural
1.25 0.90
Attachments of Substructure
DCSup: Dead Load of Structure Components and Nonstructural
1.25 0.90
Attachments of Superstructure
DD: Pile, α Tomlinson Method 1.40 0.25
Downdrag
Pile, λ Method 1.05 0.30
Drilled Shaft, O’Neill and Reese (2010) Method 1.25 0.35
DW: Dead load of Wearing Surface and Utilities 1.50 0.65
EH: Active Horizontal Earth Pressure 1.50 0.75
ESH: Earth Surcharge Horizontal Load 1.50 0.75
ESv: Earth Surcharge Vertical Load 1.35 1.00
EV: Vertical Earth Pressure 1.35 1.00

11.1.3.1 Dead Load (DCsup, DCsub, DW)

The component and wearing surface dead loads transferred from the superstructure
(DCsup and DW) to the abutment are support reactions commonly obtained from
superstructure analysis software such as CTBridge or CSiBridge. The weight of the
abutment components (backwalls, shear keys, stems, and footings), DCsub, can be easily
calculated from the geometry of the abutment. The weight of the abutment components,

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 Bridge Design Practice 11.1 • October 2022

including shear keys, is assumed to be uniformly distributed along the abutment width. In
the case of non-integral abutments, only reaction forces (vertical and horizontal) are
applied to the abutments. However, moments are also transferred from the superstructure
to the abutment for integral abutments. Figure 11.1.3-1 shows typical forces acting on a
seat-type abutment.

11.1.3.2 Live Load (LLHL93, LLPermit, LS)

Live load (LLHL93 and LLPermit) forces are typically obtained from superstructure analysis
software and are calculated as support reactions for a single lane of a truck without any
dynamic allowance (impact) for substructure analysis. There are several methods to
calculate the number of live load lanes needed for abutment design. Section 11.1.6
Design Example illustrates more details on the calculation of the number of live load
lanes.
The equivalent height of the soil (surcharge) used for the traffic load on the embankment
(Live Load Surcharge, LS) varies from 2 to 4 feet depending on the height of the
abutment, as discussed in Article 3.11.6.4. Caltrans practice is to apply the live-load
surcharge on the approach fill regardless of the presence of an approach slab.
The traffic live load acting on the backwall is only used to calculate the maximum force
effects in the backwall. This force is not considered in the analysis of other abutment
components (stem, foundations) since it is already included in the live load reaction forces
transferred from the superstructure.

LS

DCsup
DW
LL
PS

BR
CE
PS
CR Total Bearing
SH Pad Shear
TU

Figure 11.1.3-1 Typical Loads Acting on A Seat Type Abutment

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 Bridge Design Practice 11.1 • October 2022

11.1.3.3 Horizontal Loads from Superstructure (BR, CE, WS, WL, TU,
PS, CR, SH)
For the seat type abutments with elastomeric bearing pads, the total amount of horizontal
load that may be transmitted through the bearings before slippage occurs is limited to 0.2
(DCSup + DW) according to Article 3.4.5 (AASHTO-CA BDS-8). This force should be
applied in both directions (toward and away from the backwall) horizontally.

11.1.3.4 Earth Pressure Components (EH, EV, ESH, ESV)

For a cantilever abutment, the overturning forces should be balanced by the vertical earth
load on the abutment heel and the self-weight of the abutment. The AASHTO-CA BDS-8
Commentary C3.11.1 provides guidance on the selection of appropriate earth pressure
coefficients based on the relative movement of the abutment and the retained soil.

The passive earth pressure resistance exerted by the fill in front of the abutment is usually
neglected in the design due to the potential for erosion, scour, or future excavation in front
of the abutment. Furthermore, a larger relative movement is needed to activate the
passive pressure. The vertical load from the toe backfill should be included in the analysis
for overturning if it increases overturning. Figure 11.1.3-2 shows earth pressure
components acting on a typical abutment.

EV
EH

Figure 11.1.3-2 Earth Pressure Components Acting on the Abutment

11.1.3.5 Seismic Effects

Extreme Event-I (Earthquake load combination) is not considered in the design of short
seat-type abutments founded in S1 (competent) soil according to AASHTO-CA BDS
3.4.5.2. However, the global stability analysis of abutments built in the S1 (competent)
soil is not exempt from Extreme Event-I (Earthquake) load combination. Design
requirements for individual components, such as shear keys and the seat width, are still
governed by the applicable sections of the SDC 6.3, and Section 20 of the Structure

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 Bridge Design Practice 11.1 • October 2022

Technical Policies. According to SDC 6.3.4, the shear key is limited by shear capacity of
the foundation. Therefore, the shear capacity of piles under the Extreme (Earthquake)
Event load combination needs to be calculated.

For abutments in the S2 (non-competent) soil, special design provisions are required.
Such provisions should be discussed in the Type Selection meeting.

11.1.3.6 Construction Load Cases

Construction load combinations for bridge abutment design are adopted from past
practices of Caltrans working stress design and are shown in Figure 11.1.3-3. The
Construction I load combination includes the dead load of the substructure and earth load
with the surcharge calculated per AASHTO Table 3.11.6.4-1, but no superstructure loads.
Construction II load combination includes the dead load of substructure and
superstructure loads without wind, live load, and earth pressure components.

Figure 11.1.3-3 Construction Load Combinations

11.1.4 STRUCTURAL COMPONENT DESIGN CONSIDERATION

The structural design of abutment components shall be in accordance with the
requirements of Sections 5 and 6 of AASHTO-CA BDS-8. The shear keys should be
designed following SDC 6.3.4 requirements. The moment caused by eccentricity of the
loads in the transverse direction may be neglected in the analysis and design of seat-type
abutments; however, the bending moment in the transverse direction may need attention
for narrow bridges. For bridges on straight alignments with an abutment skew exceeding

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 Bridge Design Practice 11.1 • October 2022

60 degrees and for horizontally curved bridges with an abutment skew exceeding 45
degrees, A refined analysis should be performed to capture live load distributions more
accurately.

11.1.5 FOUNDATION DESIGN CONSIDERATION

The foundation design process includes sizing the spread footing and tipping the pile
foundations for tension, compression, settlement, and lateral.

11.1.5.1 Size Spread Footing

Sizing a spread footing is an iterative process, as nominal bearing resistance and
permissible net contact stress depend on the effective size of the footing. Therefore, the
geotechnical designer (GD) needs to present the permissible net contact stresses as a
group of curves for different ratios of (effective length)/ (effective width). For each load
combination, the permissible stress is extracted from the curves knowing the calculated
effective width and the effective length.

11.1.5.2 Determine Pile Tip Elevations

GD provides design tip elevations for compression, tension, settlement, and lateral. The
first two tip elevations are commonly calculated for Strength/Construction Limit States
and the settlement tip for the Service-I Limit State. For abutments in class S1 soil
supported on a single row of piles, a lateral tip is calculated by the Structural Designer
(SD) considering stability and the critical depth of the pile. The lowest design tip is
selected as the specified tip elevation and is used in the design.

11.1.5.3 Design Piles for Shear

Shear forces in the piles need to be checked for Service and Strength/Construction Limit
States. Under Service-I loads, displacement of the pile at a cut-off elevation is usually
limited to 0.25 inches. The permissible (allowable) horizontal load for a single standard
plan pile is the shear force at the cut-off elevation at 0.25 in. of the horizontal displacement
of the pile cap. Shear force developed in the pile foundation under Service-I loads shall
be less than the permissible horizontal load of the foundation. Group reduction effects
shall be considered in the calculation of the permissible horizontal load. When non-
standard piles are used in abutments, the permissible horizontal load is determined by
geotechnical analysis and considering the structural adequacy of the pile under factored
Strength/Construction loads. The horizontal component of a battered pile’s axial force
may be subtracted from the lateral load to determine the applied horizontal load on the
pile foundations.

The factored shear resistance of the pile foundation shall be compared to the factored
shear force (Strength and Construction) applied to the foundation. The shear resistance
of the foundation system is developed by the resistance of all the piles considering group

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 Bridge Design Practice 11.1 • October 2022

and batter effects. The shear resistance of a single pile is the smaller of the structural
shear resistance of the pile and the shear force applied at the cut-off elevation when the
maximum moment in a pile reaches its factored nominal flexural resistance.

11.1.5.4 Design Piles for Tension

Piles should not undergo a sustained tension under permanent loads for the Service-I
Limit State combination. If this condition occurs, the GD should be contacted to determine
if the proposed foundation type is appropriate for this condition. To ensure the structure
capacity, the SD always needs to check the structure capacity per AASHTO-CA BDS-8
Sections 5 and 6 requirements.

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 Bridge Design Practice 11.1 • October 2022

11.1.6 DESIGN EXAMPLE

The design process, including abutment live load analysis, load combinations, backwall
design, stem wall design, and footing design, for both spread footing and pile foundation,
are illustrated in the following example.

11.1.6.1 Abutment Data

The elevation and typical section of the three-span continuous post-tensioned concrete
box girder bridge are shown in Figures 11.1.6-1 and 11.1.6-2, respectively. Abutment 1
(first abutment) is considered in this example. Soil is class S1 soil.

Figure 11.1.6-1 Elevation of the Example Bridge

Figure 11.1.6-2 Typical Section of the Example Bridge

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 Bridge Design Practice 11.1 • October 2022

Plan view and typical section of the abutment are shown in Figure 11.1.6-3.

Finish Grade (FG) elevation at beginning of bridge (BB) = 16.75 ft

Average Original Grade (OG) Elevation at berm = 6.5 ft
Bottom of the footing elevation = 0 ft
Abutment height: h = 14.25 ft
Abutment length along the skew: W = 62.6 ft
Backwall height: hbw = 6.75 ft
Footing thickness: dftg = 2.5 ft
Footing length: Lftg = 64 ft
Footing width: Bftg = 10 ft
Footing toe width (footing face to face of abutment) = 3.5 ft
Depth of soil on the toe of the footing = 4.0 ft
Depth of live load surcharge on the heel is assumed dLS = 2.0 ft
Assumed edge distance (from the edge of the deck) for live load analysis = 1.0 ft (use 0
if need to consider future widening or use a width of the barrier if there is no room for
future widening.)
Total shear keys weight = 28.38 kip
Barrier weight = 0.656 kip/ ft (using the Barrier Type 842 weight)
Soil slope H:V = 2:1
End of wing wall depth = 3.0 ft
Wingwall and backwall thickness = 1.0 ft
Skew angle: θsk = 20°
Backfill soil unit weight: γs = 120 pcf
Angle of internal friction of drained backfill soil = 34°, Ka = 0.3
Pile Type – Steel Pipe 14 in. (Class 140 Alt W)
Per Standard plan B 2-5
 Compression: Nominal axial structural resistance = 280 kip
Service state = 140 kip
 Tension: Nominal axial structural resistance = 140 kip
Service state = 56 kip
Permissible horizontal load for vertical pile for this example = 27 kip (pile should have a
minimum length of 35 ft to achieve this permissible horizontal load)
Assume permissible horizontal load for battered pile = 0.6(27 kip) = 16.2 kip

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 Bridge Design Practice 11.1 • October 2022

The shear resistance of the pile group under the Extreme (Earthquake Event) = 64 kip
Concrete:
= fc' 3.6 ksi,
= γ c 150 pcf
Reinforcing steel: fy = 60 ksi

Figure 11.1-6-3a Plan View of Abutment

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 Bridge Design Practice 11.1 • October 2022

Figure 11.1-6-3b Typical Section of Abutment

11.1.6.2 Design Requirements

Perform the following design portions in accordance with AASHTO-CA BDS-8:
Calculate loads transferred from the superstructure to Abutment 1
Perform live load analysis
Calculate load combinations
Design backwall
Design stem wall
Design pile foundation
Design spread footing

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 Bridge Design Practice 11.1 • October 2022

11.1.6.3 Calculate Loads Transferred from Superstructure to

Abutment 1
The output results of the superstructure analysis using the CTBridge program (Caltrans,
2019c) for dead load (DCsup), additional dead load (DW), live load (LLHL93 and LLPermit),
and prestressing (PS) reaction forces at Abutment 1 are listed in Tables 11.1.6-1 to
11.1.6-4. The effects of other loads are neglected to simplify analysis and design
procedure.

Table 11.1.6-1 – Output of CTBridge -Dead Load Reactions

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 Bridge Design Practice 11.1 • October 2022

Table 11.1.6-3 – Output of CTBridge -Live Load Reactions

Table 11.1.6-4 – Output of CTBridge -Prestressing Reactions

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 Bridge Design Practice 11.1 • October 2022

Unfactored loads at Abutment 1 from CTBridge output are summarized as follows:

Dead Load of Superstructure (DCSup) = 772.2 kip
Addition Dead Load (DW) = 93.9 kip
Design Vehicle (LLHL93) per lane = 98.23 kip
Permit Vehicle (LLPermit) per lane = 184.01 kip
Prestress Load (PS) = 58.5 kip

11.1.6.4 Perform Live Load Analysis

The CTAbut program (Caltrans, 2022) assumes a uniform distribution of live load reaction
forces along the abutment in the transverse direction. However, localized effects
associated with the concentration of live load reaction forces at different locations of the
abutment need to be considered in the analysis. An equivalent number of live load lanes
can be calculated based on 45-degree distribution from the height of the abutment wall
at the deck to the top of the footing, as shown in Figure 11.1.6-4 (T. Zokaie et al., 2015).
When calculating an equivalent number of live load lanes, a multiple presence factor
(MPF) is multiplied by number of whole lanes that can be accommodated on the bridge.
The equivalent number of lanes, N, is calculated as:

W (nl ) ( MPF )
N= (11.1.6-1)
bn

where:
W = abutment length along the skew (62.6 ft in this example)
nl = number of whole lanes that are under consideration
bn = effective live load distribution width at the top of the footing
MPF = multiple presence factor

Per Article 3.6.1.1.1, the maximum number of design lanes that can be placed on the
bridge is determined by taking the integer part of the ratio of the clear roadway width in
feet between curbs and/or barriers then divided by 12. Furthermore, roadway widths from
20 to 24 ft should have two design lanes, each equal to one-half the roadway width.

Therefore

W cos θsk −2 ( edge distance )

nmax = (11.1.6-2)
12

The edge distance is the width of the barrier; however, it can be assumed to be zero as
the designer may need to consider future widening per Article 2.3.2.1 and use the edge
of the deck (EOD) to EOD.

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 Bridge Design Practice 11.1 • October 2022

The effective live load distribution width at the top of the footing can be written as:

     
where, an is the effective live load distribution width at the deck elevation (ft):

8 + ( edge distance ) + 12 ( n − 1)
an = (11.1.6-4)
cos θsk

h = abutment height (deck to top of the footing) (ft)

θ = angle of the load distribution (can be assumed 45 degrees)
The equivalent number of lanes, N, is calculated for different values of n varying from 1
to nmax. The maximum value of N is used in CTAbut to calculate design vehicular live
loads.

Figure 11.1.6-4 Schematics of Live Load

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 Bridge Design Practice 11.1 • October 2022

The maximum number of whole lanes:

W cos θsk − 2 ( edge distance ) 62.6cos(20o ) − 2 (1)

nmax = = 4.74 lanes
12 12

Using only the integer part: nmax = 4 lanes

Since MPF depends on the number of lanes, the designer needs to calculate the
equivalent number of lanes for each case (one, two, three,…n lanes) from Equation
11.1.6-4
For example, for two live load lanes (n = 2)

8 + (1) + 12 ( 2 − 1)
=a2 = 22.35 ft
( )
cos 20°

Height of the abutment, h = 14.25 ft

The effective width at the top of the footing is calculated by Equation 11.1.6-3 as follows:

b2= a2 + htan θ = 22.35 + (14.25 ) tan ( 45° )= 36.6 ft

The equivalent number of HL live load lanes is calculated by Equation 11.1.6-1

W ( nl )( MPF ) (=
62.6 )( 2 )(1.0 )
=N2 = 3.42 lanes
bn 36.6

Table 11.1.6-5 summarizes calculated values of an and bn for different values of n, as well
as the equivalent number of lanes, N, for HL-93 live load:

Table 11.1.6-5 Equivalent Number of HL-93 Live Load Lanes

nl an (ft) bn (ft) MPF N (lanes)
1 9.58 23.83 1.2 3.15
2 22.35 36.60 1.0 3.42
3 35.12 49.37 0.85 3.23
4 47.89 62.14 0.65 2.62

In this example, two lanes result in the largest number of equivalent lanes. Therefore, an
equivalent number of live load lanes for HL-93 truck, N, is taken as 3.42 lanes.

The same method is used for permit trucks; however, the designer should consider only
one or two lanes of P truck with MPF of one used for both cases.

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 Bridge Design Practice 11.1 • October 2022

Table 11.1.6-6 provides a summary of calculations for the number of Permit Truck live
load lanes.

Table 11.1.6-6 Equivalent Number of Permit Truck Live Load Lanes

nl an (ft) bn (ft) MPF N(lanes)
1 9.58 23.83 1.0 2.63
2 22.35 36.60 1.0 3.42

The equivalent number of live load lanes for permit truck is 3.42 lanes which is calculated
by placing two lanes side by side.

In summary, design live loads are calculated as:

• Design truck (LLHL93) load for the abutment design:

LLHL93 = ( equivalent number of lanes )(HL93 design vehicular load per lane )

(=
3.42 lanes )( 98.23 kip/lane ) 335.95 kip

• Permit truck load for abutment design:

LLPermit = ( equivalent number of lanes )(Permit truck load per lane )

(=
3.42 lanes )(184.01 kips/lane ) 629.31 kip

11.1.6.5 Calculate Load Combinations

The permanent loads, including the weight of the different components and the soil
pressure exerted on the abutment are calculated as follows. Figure 11.1.6-5 shows how
the abutment is broken down into several components and also shows forces acting on
those components.

Sample calculations of unfactored forces are shown as follows:

Weight of the footing, W1:

=W1 Lftg Bftg=

dftg γ c ( 64 )(10 )( 2.5 )(=
0.15 ) 240.0 kip

Weight of the soil behind the stem wall, V1

V=
1 (16.75 − 2.5 )(10 − 3.5 − 4.0 ) ( 62.6-2 (1) ) ( 0.12=
) 259.1 kip
Active soil pressure behind the abutment, H1:

Chapter 11.1 Abutments 11.1-21

© 2022 California Department of Transportation. ALL RIGHTS reserved.
 Bridge Design Practice 11.1 • October 2022

(=
h + dftg ) WK a γ s (14.25 + 2.5 )2 ( 62.6 )( 0.3 )( 0.12 )
2

=H1 = 316.1 kip

2 2

Horizontal active live load surcharge on abutment, LS1:

=
LS1 (
dLS h + dftg WK= )
a γs ( 2 )(14.25 + 2.5 )( 62.6 )( 0.3 )( 0.12
= ) 75.5 kip

Vertical live load surcharge on the heel, LSvertical:

= dLS ( heel side width )=

LSvertical Lγ s ( 2 )(10 − 4 − 3.5 )( 64 )( 0.12 )
= 38.4 kip

The equivalent bearing pad shear, Vpad, is assumed as 20% of (DCSup + DW).

V=
pad (
0.2 DCsup + DW )
= 0.2 ( 772.2 + 93.9
=) 173.22 kip

W3 DC, DW, LL
LS3
H3
Pad Shear

LS2 V1
LS1 W2
H2
V2
H1

H4
W1
X
(0,0)

Figure 11.1.6-5a Schematics of Forces Acting to the Abutment

11.1-22 Chapter 11.1 Abutments

© 2022 California Department of Transportation. ALL RIGHTS reserved.
 Bridge Design Practice 11.1 • October 2022

Vww2

Vww3
Vww1

Figure 11.1.6-5b Schematics of Forces Acting to the Abutment

Table 11.1.6-7 shows the summary of unfactored forces and coordinates of their
application points in the system of coordinates shown in Figure 11.1.6.5a. The moment
arm is calculated with respect to the point to be used in design calculations. For example,
for backwall design, the moment should be calculated about the center of the base of the
backwall. Therefore, the reference point will be the centerline of the backwall at the base,
and moment arms are calculated by subtracting the coordinates of the reference point
from the coordinates of the point of the application. To simplify dead load calculations of
the wingwall, it is divided into three parts, as shown in Figure 11.1.6-5b.

Chapter 11.1 Abutments 11.1-23

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 Bridge Design Practice 11.1 • October 2022

Table 11.1.6-7 Summary of Unfactored Loads and Points of Application

Moment Arm (clockwise
Coordinates (ft)
Unfactored Loads positive) (ft)
(kip) Backwall Stem Footing
x y
Check Check CL
W1 240.0 5.00 0.00
W2 281.7 4.50 0.00 -0.50
W3 63.4 3.00 0.00 -1.50 -2.00
DC 772.2 5.00 0.50 0.00
DW 93.9 5.00 0.50 0.00
Vpad 173.22 10.00 0.00 7.50 10.00
PS 58.50 5.00 0.50 0.00
V1 259.1 1.25 -3.75
V2 107.5 8.25 3.25
V3 6.1 2.937 -2.063
LSVertical 38.4 1.25 -3.75
Vkeys 28.4 5.00 0.50 0.00
Vww1 10.7 1.25 -3.25 -3.75
Vww2 11.7 -6.50 -11.00 -11.50
Vww3 21.9 -4.33 -8.83 -9.33
Vbarrier 21.65 -4.75 -9.25 -9.75
H1 316.1 5.58 5.58
H2 228.8 7.25 4.75
H3 51.3 12.25 2.25
H4 0.0 2.167 1.33 2.167
LS3 30.4 13.375 3.375
LS2 64.2 9.625 7.125
LS1 75.5 8.375 8.375

Note: LSVertical is the vertical force due to the live load surcharge acting on the heel side
of the footing. Vbarrier is the weight of the barrier acting at the top of the wingwall. H4 is
equal to zero because the passive pressure coefficient, Kp, is assumed to be zero in this
example. Historically, the passive pressure for a short seat abutment design is ignored in
Caltrans practice for several reasons. The first reason is that the quality of the backfill in
front of the abutment is unknown, and the soil in this area would be eroded during the life
of the bridge. The second reason is that a large movement is needed in order for passive
soil to engage. The designer should consult with GD for the value of Kp if passive soil
pressure needs to be considered.

11.1-24 Chapter 11.1 Abutments

© 2022 California Department of Transportation. ALL RIGHTS reserved.
 Bridge Design Practice 11.1 • October 2022

The load factor for the bearing pad shear is either 0 or 1.25. The bearing pad shear should
be applied in both directions horizontally to capture the worst effect for each component.
Tables 11.1.3-1 and 11.1.3-2 summarize load factors to be used for abutment design.
Considering the large number of loads to be considered use of engineering judgement to
identify governing cases for the design of each component is not practical. CTAbut
examines all possible combinations and reports the governing cases that produce the
largest Demand-to-Capacity (D/C) ratio for each check. In this example, the governing
load cases have been extracted from CTAbut to show the design process.

11.1.6.6 Design Backwall

For the backwall design, the design loads are the weight of the backwall, the horizontal
surcharge live load, and the horizontal soil pressure acting on the backwall. The wheel
loads on the backwall are not considered in this example.

11.1.6.6.1 Calculate Factored Load Effects

The backwall can be easily analyzed as a cantilever beam to calculate factored load
effects for different load combinations:

Strength Limit State

There are two load factors for the substructure dead load, 0.9 and 1.25.

The vertical axial load at the backwall can either be:

Pbw = 0.9 W3 = 0.9(63.4) = 57.1 kip, or

Pbw = 1.25 W3 = 1.25(63.4) = 79.3 kip
However, the effect of axial load is negligible in the backwall design.

The horizontal earth pressure, EH (shown as H3), has two load factors, 0.75 and 1.5. The
factor for the horizontal live load surcharge, LS3, is 1.75. Design shear force for the
backwall is calculated based on the greatest effect, which is:

Vbw = 1.5 H3 + 1.75 LS3 = 1.5(51.3) + 1.75(30.4) = 130.2 kip

Similarly, the governing factored moment for the backwall design is calculated using the
upper limits of contributing loads (W3, H3, and LS3). However, W3 does not produce a
bending moment, therefore:

h   hbw 
=Mbw 1.5H3  bw  + 1.75LS3  2 
 3   
 6.75   6.75 
=(1.5 )( 51.3 )   + (1.75 )( 30.4 )   =352.7 kip-ft
 3   2 

Chapter 11.1 Abutments 11.1-25

© 2022 California Department of Transportation. ALL RIGHTS reserved.
 Bridge Design Practice 11.1 • October 2022

Service Limit State

The load factors are one for Service Limit State, and only a service moment is needed for
the crack control check:
 hbw   hbw 
=Mservice (1.00)) H3   + (1.00 ) LS3  2 
 3   
 6.75   6.75 
= (1.0 )( 51.3 )   + (1.0 )( 30.4 )   = 218.0 kip-ft
 3   2 

11.1.6.6.2 Design for Flexure

The backwall thickness of dbw = 12 in. is used to check the following factored
moments acting per unit length of the backwall

352.7
=
Mu = 5.63 kip-ft/ft
62.6
218.0
M=
service = 3.48 kip-ft/ft
62.6

Assume:

• Vertical rebar #7 spacing at 12 in.

• Concrete cover = 2 in.
• Bar diameter, dbd = 1.0 in.
• Area of the bar As= 0.60 in.2

Factored Flexural Resistance

The factored flexural resistance is calculated in accordance with Articles 5.6.3.2 and
5.6.3.3 as follows:

The area of steel contributing to unit width of the backwall

(12 )
=As ( 0.60
= ) 0.60 in.2
(12 )
Per article 5.6.2.2, the coefficient, β1, is taken as 0.85 for f′c = 3.6 ksi and α1 is 0.85.
Neglecting compression steel, the distance between the neutral axis and the depth of the
concrete stress block is obtained:

=c =
As fy ( 0.60 )( 60
=
) 1.153 in.
0.85fc' β1b ( 0.85 )( 3.6 )( 0.85 )(12 )

11.1-26 Chapter 11.1 Abutments

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 Bridge Design Practice 11.1 • October 2022

a = cβ1 = (1.153 )( 0.85 ) = 0.98 in.

Distance from the extreme compression fiber to the centroid of nonprestressed tensile
reinforcement:

d bd 1.0
de = d bw − (concrete cover) − = 12 − 2 − = 9.5 in.
2 2

The net tensile strain in the extreme tension steel reinforcement is calculated as follows:

0.003 ( de − c ) ( 0.003 )( 9.5 − 1.153 )

=εs = = 0.0217
c 1.153

Since the calculated strain εs is larger than 0.005, the section is considered as tension-
controlled, and a resistance factor φ is 0.9 (AASHTO-CA BDS 5.5.4.2). The factored
flexural resistance is calculated as:

 a 0.98 
Mr =
φMn = ( )( 0.9 )( 0.60 )( 60 )  9.5 −
φ As fy  de −  =
 2  2 

= 291.92 =
kip-in. 24.33 kip-ft=
> Mu 5.63 kip-ft OK

Therefore, the selected number of bars is adequate for strength

Minimum Reinforcement

Article 5.6.3.3 requires a minimum amount of reinforcement to be provided for crack

control. The factored flexural resistance Mr is required to be at least equal to the smaller
of Mcr and 1.33 Mu as follows (gross section properties are used instead of transformed
sections):

Modulus of rupture: =fr 0.24

= fc' 0.24
= 3.6 0.455 ksi

2
=
(12 )(12 )= 288 in.3
Gross section modulus: Sc S=
nc
6

Flexural cracking variability factor: γ1 = 1.6 for all concrete structures except precast
segmental structures per Article 5.6.3.3.

The ratio of specified minimum yield strength to ultimate tensile strength of the
reinforcement: γ3 = 0.75 for A706, Grade 60 reinforcement per Article 5.6.3.3. The
calculations are as follows:

Chapter 11.1 Abutments 11.1-27

© 2022 California Department of Transportation. ALL RIGHTS reserved.
 Bridge Design Practice 11.1 • October 2022

Mcr =γ 3 γ1fr Sc
(AASHTO 5.6.3.3-1)
= (0.75)(1.6)(0.455)(288)
= 157.25 =kip-in 13.10 kip-ft

1.33Mu 1.33(5.63)
= = 7.49 kip-ft

Mcr = 13.10 
Mr = 24.38 kip-ft > smaller of 
φMn = =7.49 kip-ft (AASHTO 5.6.3.3)
1.33M u = 7.49 

Crack Control

AASHTO Article 5.6.7 requires maximum limits of rebar spacing for crack control.

700 γ e
s ≤ − 2dc (AASHTO 5.6.7-1)
βs fss

Assuming exposure factor γe is equal to 1 (class-I exposure), and dc is equal to 2.5 in.

dc 2.5
βs = 1 + = 1+ = 1.376
0.7(h − dc ) ( 0.7 )(12 − 2.5 )
The cracked concrete section is used to calculate tensile stress in steel reinforcement
under service loads, and the moment of inertia for unit width (12 in.) of the transformed
section (based on concrete), Itr, is calculated as follows:

Ec = 33,000K1w c1.5 fc' (AASHTO C5.4.2.4-2)

1.5
= (33,000)(1.0)(0.15)
= 3.6 3637 ksi

Es 29,000
=
n = = 7.97
Ec 3,637

Usually, n is rounded to the nearest integer number. Therefore, n = 8 will be used.

As 0.60
=
ρ = = 0.0053
bde (12 )( 9.5 )
2
k= ( ρn ) + 2 ( ρn ) − ρn
2
= ((0.0053)(8)) + 2(0.0053)(8) − (0.0053)(8)= 0.252

k=
de =
kd e ( 0.252 )( 9.5
= ) 2.394 in.

11.1-28 Chapter 11.1 Abutments

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 Bridge Design Practice 11.1 • October 2022

bk 3 2
Itr = de + n As ( de − kde )
3
3
(12 )( 2.394 ) + ( 8 )( 0.60 )( 9.5 − 2.394
2
= = ) 297.26 in.
3

Tensile stress in steel reinforcement at the service limit state is calculated as:

Ms ( de − kde ) ( 3.48 )(12 )( 9.5 − 2.394 )

=fss n= (8) = 7.99ksi -use 8 ksi
Itr 297.26

The maximum spacing is checked as (Article 5.6.7-1):

700 γ e 700(1)
s= 12 in. ≤ − 2dc= − 2(2.5)= 58.59 in. OK
βs fss (1.376)(8)

Therefore, the #7 bar at a spacing of 12 in. is acceptable.

For backwall, b = 12 in. (unit width) and backwall height h = 6.75 ft = 81 inches, the
horizontal shrinkage and temperature reinforcement per unit foot width shall satisfy the
following equations (Article 5.10.6):

1.3bh 1.3(12)(81)
As ≥ = = 0.113 in.2 (AASHTO 5.10.6-1)
2(b + h )fy 2(12 + 81)(60)

0.11 in.2 ≤ As ≤ 0.6 in.2 (AASHTO 5.10.6-2)

Assume horizontal temperature bars of #4 @ 12 in. As = 0.1963 in.2;

=As 0.1963 in.2 > 0.113 in.2 OK

2
0.11 in.= ≤ As 0.1963 in.2 ≤ 0.6 in.2 OK

Using temperature bars of #4 @ 12” is acceptable.

11.1.6.6.3 Design for Shear

The shear design for the abutment backwall is usually based on the shear resistance of
the concrete alone. The backwall is not heavily reinforced since it is designed to break
during a seismic event. The design procedure is the same as the steam wall shown in
Section 11.1.6.7.3 and is not repeated herein.

Chapter 11.1 Abutments 11.1-29

© 2022 California Department of Transportation. ALL RIGHTS reserved.
 Bridge Design Practice 11.1 • October 2022

11.1.6.7 Design Stem Wall

11.1.6.7.1 Calculate Factored Load Effects

The weights of backwall, stem wall, wing walls, shear keys, superstructure (DCsup),
wearing surface, and utilities load (DW), as well as the design truck (HL93) and the permit
truck (Permit), are vertical gravity loads applied to the stem wall. The bearing pad shear
load, prestressing load (PS), horizontal pressure by live load surcharge, horizontal active
soil pressure from the back of stem wall and backwall, and the horizontal passive soil
pressure from the fill in front of the stem wall (this passive pressure may be conservatively
ignored for short seat abutments however it is considered for tall cantilever abutments)
are horizontal loads that are considered in stem wall design.

Similar to the backwall, thirteen permanent loads are considered in the stem wall design,
which result in a very high number of possible load combinations. CTAbut is used to
identify controlling load combinations in this design example. CTAbut prints out the load
factors for controlling combinations to be used for the design of each component of the
abutment at the end of the full report. Tables 11.1.6-8 and 11.1.6-9 show the values of
load factors for governing cases for stem wall design.

Table 11.1.6-8 Load Factors for Strength and Construction Limit States

Stem Pad
DCSup. DCSub. DW PS LLHL93 LLPermit EHa LSh EHp Comb.
wall* shear+
Pmax 1.25 1.25 1.50 1.00 1.25 0.00 1.35 1.50 0.00 - STR2
Vmax(B) 1.25 0.90 1.50 1.00 1.25 1.75 0.00 1.50 1.75 - STR1
Mmax(B) 1.25 0.90 1.50 1.00 1.25 1.75 0.00 1.50 1.75 - STR1
Vmax(F) 0.90 1.25 0.65 1.00 -1.25 0.00 1.35 0.75 0.00 - STR2
Mmax(F) 0.90 1.25 0.65 1.00 -1.25 0.00 1.35 0.75 0.00 - STR2
*B = Back face of the stem wall in tension; F = Front face of the stem wall in tension
+Negative gamma factor for Pad shear has been applied to capture bi-directional force effects

Table 11.1.6-9 Load Factors for Service Limit State

Stem Pad
DCSup. DCSub. DW PS LLHL93 LLPermit EHa LSh EHp Comb.
wall shear
Mmax(B) 1.0 1.0 1.0 1.0 1.0 1.0 0 1.0 1.0 - SER1
Mmax(F) 1.0 1.0 1.0 1.0 -1.0 1.0 0 1.0 1.0 - SER1

All the controlling factored design loads could be calculated by using the tables above.
For example, the factored design shear for the stem wall is calculated as:

Vmax ( B=
) 1.25Vpad + 1.5H2 + 1.75LS2

= 1.25 (173.2 ) + 1.5 ( 228.8 ) + 1.75 ( 64.2 ) = 672.1 kip

11.1-30 Chapter 11.1 Abutments

© 2022 California Department of Transportation. ALL RIGHTS reserved.
 Bridge Design Practice 11.1 • October 2022

Summary of factored loads effects for the stem wall design are given in Table 11.1.6-10.

Table 11.1.6-10 Factored Load Effects for Stem Wall

Mmax(B) (kip-ft) 4356.80
Strength
Mmax(F) (kip-ft) 1199.47
Limit State
Vmax(B) (kip) 672.1

Service Mmax(B) (kip-ft) 2835.55

Limit State Mmax(F) (kip-ft) 0.00

Irrespective of the direction, the maximum calculated shear is used for the design of the
shear reinforcement in the stem wall. The designer should check both faces (the heel
side and the toe side) when designing the shear reinforcement if the concrete cover is
different. CTAbut reports some cases as 0.00 if the compression or tension does not
affect the section.

11.1.6.7.2 Design for Flexure

An axial force is not usually considered in the flexural design of the stem wall since the
effect is often minimal. The effect of the moment acting in the transverse direction (biaxial
bending) is also negligible. However, in the case of narrow abutments (i.e., single lane on
or off-ramp), Article 5.6.4.5 requirements shall be satisfied.

The design procedure for flexural, crack control, and shrinkage and temperature
reinforcement is the same as the backwall and is not repeated here. However, the detailed
steps for the shear design are shown in the next section.

11.1.6.7.3 Design for Shear

The shear design for the abutment stem wall and footing follows the General Procedure
per Article 5.7.3.4.2 and its CA amendment. The flowchart of the process in CTAbut is
shown in figure 11.1.6-6, and the shear design for the stem wall follows.

The following variable would be needed to calculate the shear:

d = 48 in.

β1 = 0.85

bv = 62.6(12) = 751.2 in.

#7 @ 12 vertical bars total 64 bars is used.

Hence, As = (64)(0.6) = 38.4 in.2

Chapter 11.1 Abutments 11.1-31

© 2022 California Department of Transportation. ALL RIGHTS reserved.
 Bridge Design Practice 11.1 • October 2022

Checking Shear
Capacity

Is the min. shear

reinforcement specified
in AASHTO 5.7.2.5
No
Yes provided?

Use general procedure

and equation 5.7.3.3-3
& 4 with parameter (β,θ)
Use general procedure
from Table B5.2-2
and equations 5.7.3.3-3
& 4 with parameters (β,
θ) from Table B5.2-1

Is
Is Add shear
Add shear Continues with Vu ≤ φVn?
Vu ≤ φVn? Yes No reinforcement
reinforcement No check See 5.7.3.3
See 5.7.3.3 and recheck
and recheck For Vn
For Vn

Yes

Use general procedure

and equation 5.7.3.3-3
& 4 with parameter (β,θ)
from Table B5.2-2

No shear Is Check spacing of

reinforcement Yes Vu ≤ φVc? No shear reinforcement
required per AASHTO 5.7.2.6

Figure 11.1.6-6 Shear Design Flowchart

11.1-32 Chapter 11.1 Abutments

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 Bridge Design Practice 11.1 • October 2022

As fy (38.4)(60)
=c = '
= 1.18
α1fc β1b (0.85)(3.6)(0.85)(751.2)

a = cβ1 =(1.18)(0.85) = 1.00

bar diameter 1
de= 48 – concrete cover – = 48 − 2 − = 45.5 in.
2 2

Assume there is no shear reinforcement, Av = 0.

The minimum transverse reinforcement requirement from Article 5.7.2.5-1 is not satisfied.

The effective shear depth:

a 1
dv = d e − = 45.5 − = 45.0
2 2

Per AASHTO Article 5.7.2.8: dv need not be taken to be less than the greater of

0.9 de = 0.9 (45.5) = 40.95 in.

or 0.72 h = 0.72 (48) = 34.56 in.

since 0.9 de and 0.72 h is smaller than dv, dv = 45.0 in.

=Vc 0.0316βλ fc' bv dv (AASHTO 5.7.3.3-3)

Av fy dv (cot θ + cot α )sin α

Vs = (AASHTO 5.7.3.3-4)
s

α = 90° and above equation reduces to

Av fy dv cot θ
Vs = (AASHTO C5.7.3.3-1)
s

Using Table B5.2-2, θ and β could be obtained.

Since the section contains less than the minimum transverse reinforcement as specified
in Article 5.7.2.5, equation B5.2-4 would be used to obtain the εx.

 Mu 
 + 0.5Nu + 0.5 Vu − Vp cot θ − Aps fpo 
d
ε x = v  (AASHTO B5.2-4)
Es As + E p Aps

Chapter 11.1 Abutments 11.1-33

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 Bridge Design Practice 11.1 • October 2022

Since there is no prestressing reinforcement, the equation reduces to

 Mu 
 + 0.5Nu + 0.5 Vu cot θ 
d
ε x = v  (11.1.6.1-1)
Es As

Per AASHTO CB5.2, 0.5 cot θ could be assumed 1 for the first trial to limit a trial
and error process.

 Mu 
 + 0.5Nu + Vu 
d
ε x = v  (11.1.6.1-2)
Es As

CTAbut checks both Vumax with its associated moment and Mumax with its associated shear
for each section of the component.

Table 11.1.6.1-2 Stem Wall Back Section Loads to Calculate the Shear Reinforcement
Vumax = 672.1 kip VuM = -4356.80 kip-ft VuN = - 2148.00 kip
Mumax = -4356.80 kip-ft MuV = 672.1 kip MuN = - 2148.00 kip

In this example, the associated moment or shear is exceptionally equal to the controlling
values.

 −4356.80 
 + 0.5( −2148.00) + 672.1 
 = 3.75  0.6824 * 10−3
εx
(29000)(38.4)

 1.38   1.38 
=s xe s x  =  (3.75)(12)  =  38.10 in. ≤ 80 in. OK
 ag + 0.63   1 + 0.63 
 

θ = 53.7 and β =1.66 using AASHTO Table B5.2-2 for εx ≤ 1.5 and sxe≤40.

'
=Vc 0.0316βλ f=
c bv dv 0.0316(1.66)(1.0) 3.6(751.2)(45.0)
= 3364.45 kip

Vs = 0 since initially, they are no shear reinforcement

φVn = φ(Vc + Vs )
Lesser of  '
φ(0.25)fc bv dv

11.1-34 Chapter 11.1 Abutments

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 Bridge Design Practice 11.1 • October 2022

φ(0.25)fc' bv dv =
φVn = (0.9)(0.25)(3.6)(751.2)(45.0) =
27381.24 kip

φ(Vc + Vs ) =
φVn = 0.9(3364.45 + 0) =
3028.00 kip (controlled)
Vu max 672.1 kip
= = < φVn 3028.00 kip
No shear reinforcement is required for the stem wall.

11.1.6.8 Design Pile Foundation

11.1.6.8.1 Select Piles

The standard Class 140 piles are selected in this example, where the diameter of the pile
is 14 in. with a batter of 1 to 3. There are two rows of piles with 13 piles in each row which
brings the total number of piles to 26. One row of piles is battered. The distances to the
center of the pile from footing heel are 2 ft and 8 ft for Rows 1 and 2, respectively.

11.1.6.8.2 Calculate Factored Load Effects

Using controlling load combinations from CTAbut output, shown in Tables 11.1.6-11 and
11.1.6-12, the factored loads for pile group design are calculated. The summary of
factored loads is shown in Table 11.1.6-13.

Table 11.1.6-11 Load Factor for Strength Limit State and Construction Combination

Pile DCSup. DCSub. DW PS Pad LLHL93 LLPermit EHa LSh EHp EVa EVp LSv Comb.
Group* shear
Pmax(C) 1.25 1.25 1.50 1.00 1.25 0 1.35 1.50 0 - 1.35 1.35 0 STR2
Pmax(T) 0 0.90 0 0 0 0 0 1.50 0 - 1.00 1.00 0 CON1
FRow(T) 0.90 0.90 0.65 1.00 1.25 1.75 0 1.50 1.75 - 1.00 1.35 0 STR1
FRow(C) 1.25 1.25 1.50 1.00 -1.25 0 1.35 0.75 0 - 1.35 1.00 0 STR2
LRow(T) - - - - - - - - - - - - - -
LRow(C) 1.25 1.25 1.50 1.00 1.25 1.75 0 1.50 1.75 - 1.00 1.35 0 STR1
*FRow: First row from Heel, LRow: Last row from Heel, T: Tension, C: Compression

Table 11.1.6-12 Load Factors for Service Limit State

Pile DCSup. DCSub. DW PS Pad LLHL93 LLPermit EHa LSh EHp EVa EVp LSv Comb.
Group shear
Pmax(C) 1.0 1.0 1.0 1.0 1.0 1.0 0 1.0 1.0 - 1.0 1.0 1.0 SER1
Pmax(T) 1.0 1.0 1.0 1.0 1.0 1.0 0 1.0 1.0 - 1.0 1.0 1.0 SER1
LatDC+ 1.0 1.0 1.0 1.0 1.0 1.0 0 1.0 1.0 - 1.0 1.0 1.0 SER1
FRow(T) - - - - - - - - - - - - - -
FRow(C) 1.0 1.0 1.0 1.0 -1.0 1.0 0 1.0 1.0 - 1.0 1.0 1.0 SER1
LRow(T) - - - - - - - - - - - - - -
LRow(C) 1.0 1.0 1.0 1.0 1.0 1.0 0 1.0 1.0 - 1.0 1.0 1.0 SER1
+LatDC: DC ratio of entire pile group lateral resistance capacity

Chapter 11.1 Abutments 11.1-35

© 2022 California Department of Transportation. ALL RIGHTS reserved.
 Bridge Design Practice 11.1 • October 2022

Table 11.1.6-13 – Summary of Factored Load Effects for Pile Group Design
P (axial load) V ( shear) M (moment)
Pile Group
kip kip kip-ft
Pmax(C) 3366.65 690.73 2883.45
Strength Pmax(T) 984.22 474.21 1240.67
Limit FRow(T) 1836.37 822.85 4634.71
State FRow(C) 3329.01 20.58 -2893.18
LRow(C) 3012.17 822.85 4334.39
Pmax(C) 2351.11 564.85 2492.79
Service Pmax(T) 2015.16 564.85 2492.79
Limit LatDC 2015.16 564.85 2492.79
State FRow(C) 2351.11 218.41 -971.61
LRow(C) 2351.11 564.85 2492.79

11.1.6.8.3 Check Strength Limit State

The resistance of Class 140 standard piles is given in Standard Plan B2-5 as the nominal
axial structure resistance of 280 kip for the compression and the nominal axial structure
resistance of 140 kip for the tension.

The geotechnical resistance factor (φ) is reported by Geotechnical Services on the

Foundation Design Recommendations table and is assumed 0.7 for the Strength Limit
State. The designer needs to compare the factored load on the pile with the factored
nominal axial resistance, which is the geotechnical capacity of the pile under the Strength
Limit State. The factored nominal axial resistance (geotechnical) for standard plan piles
can be assumed as 0.7 (nominal axial structural resistance), that is 0.7(280) = 196 kip for
the compression and 0.7(140) = 98 kip for the tension.

The calculation of the moment of inertia of pile group, I, is shown in table 11.1.6-14.

Where np is the number of piles in each row; d is the distance from the face of footing (toe
side), and equivalent Cgpile is the center of gravity for the pile group from the footing toe.

Table 11.1.6-14 Calculation of Moment of Inertia

npd (ft) I = np(d - Cgpile)2 (ft2)
Row 1 13(2) = 26 13(2 -5)2=117
Row 2 13(8) = 104 13(8-5)2 = 117
∑= 130 234

The center of the gravity of the pile group from the toe of the footing (Cgpile) = 130/26 =
5.0 ft which is the center line of footing since the number of piles in each row are the
same.

The moment of inertia is evaluated as I = 234 ft2, as shown in Table 11.1.6-14.

The pile reaction force is calculated as follows.

The axial force of any vertical pile is calculated from Ppile = P/np ± Mc/I, where c is the

11.1-36 Chapter 11.1 Abutments

© 2022 California Department of Transportation. ALL RIGHTS reserved.
 Bridge Design Practice 11.1 • October 2022

distance between the centerline of the pile and the center of gravity of the pile group.

As an example, the last row pile reaction (maximum that is used in the design) is
calculated as:

3012.17 4334.39 ( 5 − 2 )
PLRow (C ) = + 171.4 kip
=
26 234

Since the pile reaction force is less than factored nominal resistance in the compression
(186.0 kip), it is acceptable. This check is needed for each load combination and for each
row of the piles.

The summary of pile reactions for the strength limit state is shown in Table 11.1.6-15

Table 11.1.6-15 – Summary of Pile Axial Design

Factored
Factored Load Factored Resistance
Load/Factored Check
(kip) (kip)
Resistance ratio
Row 1 165.1 196.0 165.1/196.0= 0.84 Less than 1- OK
Row 2 171.4 186.0 171.4/186.0 =0.92 Less than 1- OK

(196)(3)
where: the factored vertical resistance of battered pile = = 186.0 kip .
2 2
1 +3

The permissible horizontal (lateral) load of the pile group under the service limit state shall
also be checked. The permissible horizontal load for a single pile assuming 5 feet of the
embedment and zero axial force is 27 kip, and the reduction factor for battered piles is
taken as 0.6 for this example.

Permissible horizontal resistance of all piles, Lr

27 ( number of vertical piles ) + 27 ( batter factor )( number of battered piles )
27(13) + 27(0.6)(13) =
= 561.6 kip

Controlling Service Limit State (LatDC) pile group:

P = 2015.16 kip and M = 2492.79 kip-ft

2015.16 2492.79 ( 5 − 2 )
PFRow (C ) = + 109.47 kip
=
26 234
109.47
=
Horizontal reaction force of a batter pile = 36.49 kip
3

Horizontal reaction force of all battered piles, Fpile = (36.49)(13) = 474.30 kip

Total Maximum Lateral load under Service Limit State, Fx = 564.85 kip

Chapter 11.1 Abutments 11.1-37

© 2022 California Department of Transportation. ALL RIGHTS reserved.
 Bridge Design Practice 11.1 • October 2022

Required horizontal load = Total maximum lateral load – horizontal reaction force of all
batter piles = 564.85 – 474.30 = 90.55 kip

The permissible horizontal load (561.6 kip) is greater than required horizontal load (90.55
kip). Therefore, it is acceptable. The designer also needs to check the Construction II
combination; however, that combination usually does not govern.

Note - This example is to show the designer the use of batter piles. The demand/capacity
for this example is extremally low, perhaps, the pile may not need to be battered for this
example.

11.1.6.8.4 Communicate with Geotechnical Designer

Under the Service I Limit State, both total and the permanent support loads (calculated
as net) are reported to GD:

Total Load (net) = Maximum load under Service-I – the weight of the overburden soil

Total Load ( net

= ) 2351.11 − (OG − BOF ) Lftg Bftg γ s

= 2351.11 − ( 6.5 − 0 )( 64 )(10 )( 0.12

= ) 1851.91 kip
The permanent load (net) = Total Load – Live Load – Live Load Surcharge (if any)

The permanent load (net) = 1851.91 - 336.0 - 38.4 = 1477.5 kip. Under the Strength Limit
State, the maximum force per support, the minimum force per support, also the maximum
compression, and the tension force per pile are reported:

The maximum force per support = 3366.65 kip

The maximum compression load per pile = 171.4 kip

There is no tension in a pile for this example. The General Foundation information to be
sent from SD to GD is shown in Table 11.1.6-16.
Table 11.1.6-16a Information to be Provided to GD
Foundation Design Data Sheet

Finished Pile Cap Size Permissible

Cut-off Number of
Support Grade (ft) Settlement
Pile Type Elevation Piles per
No. Elevation Under Service
(ft) Support
(ft) B L Load (in)
Abut 1 Class 140 16.75 0.5 10 64 1” 26
Bent 2
Bent 3
Abut 4 Class 140 16.75 0.5 10 64 1” 26

11.1-38 Chapter 11.1 Abutments

© 2022 California Department of Transportation. ALL RIGHTS reserved.
 Bridge Design Practice 11.1 • October 2022

Table 11.1.6-16b Loads to be Provided to GD

Foundation Factored Design Loads
Strength Limit State Extreme Event Limit State
Service –I Limit State
(Controlling Group, kip) (Controlling Group, kip)

Support Compression Tension Compression Tension

Total
No. Permanent
Load
Loads per Max Max Max Max
per Per Per Per Per
Support Per Per Per Per
Support Support Support Support Support
Pile Pile Pile Pile
Abut 1 1852 1478 3367 171 0 0 N/A N/A N/A N/A
Bent 2
Bent 3
Abut 4 1852 1478 3367 171 0 0 N/A N/A N/A N/A

Note -Since this design example is for abutment design, information on bents is not shown.

11.1.6.8.5 Design Pile Cap

Tables 11.1.6-17 and 11.1.6-18 summarize the load factors for the controlling load
combinations for the design of the pile cap.

Table 11.1.6-17 Load Factors for Strength Limit State

Pile Cap Pad
DCSup. DCSub. DW PS LLHL93 LLPermit EHa LSh EHp EVa EVp LSv Comb.
Sections shear
MTopHel 0.90 0.90 0.65 1.00 1.25 1.75 0 1.50 1.75 - 1.35 1.35 1.75 STR1
VTopHel 0.90 0.90 0.65 1.00 1.25 1.75 0 1.50 1.75 - 1.00 1.35 0 STR1
MBotHel 1.25 1.25 1.50 1.00 -1.25 0 1.35 0.75 0 - 1.00 1.00 0 STR2
VBotHel 1.25 1.25 1.50 1.00 -1.25 0 1.35 0.75 0 - 1.35 1.00 0 STR2
MTopToe 0 0.90 0 0 0 0 0 0.75 0 - 1.35 1.35 0 CON1
VTopToe 0 0.90 0 0 0 0 0 0.75 0 - 1.35 1.00 0 CON1
MBotToe 1.25 1.25 1.50 1.00 1.25 1.75 0 1.50 1.75 - 1.00 1.00 0 STR1
VBotToe 1.25 1.25 1.50 1.00 1.25 1.75 0 1.50 1.75 - 1.00 1.35 0 STR1

Table 11.1.6-18 Load Factors for Service Limit State

Pile Cap Pad
DCSup. DCSub. DW PS LLHL93 LLPermit EHa LSh EHp EVa EVp LSv Comb.
Sections shear
MTopHel 1.00 1.00 1.00 1.00 1.00 1.00 0 1.00 1.00 - 1.00 1.00 1.00 SER1
MBotHel 1.00 1.00 1.00 1.00 -1.00 1.00 0 1.00 1.00 - 1.00 1.00 1.00 SER1
MTopToe 1.00 1.00 1.00 1.00 -1.00 1.00 0 1.00 1.00 - 1.00 1.00 1.00 SER1
MBotToe 1.00 1.00 1.00 1.00 1.00 1.00 0 1.00 1.00 - 1.00 1.00 1.00 SER1

Using the information shown in Tables 11.1.6-17 and 11.1.6-18, the factored loads for the
pile cap are calculated. The summary of factored loads shown in Table 11.1.6-19 is used
for the top and bottom reinforcement design as well as the shear design.

Chapter 11.1 Abutments 11.1-39

© 2022 California Department of Transportation. ALL RIGHTS reserved.
 Bridge Design Practice 11.1 • October 2022

Table 11.1.6-19 Summary of Factored Loads

P (axial load) V ( shear) M (moment)
Pile Cap Sections
kip kip kip-ft
MTopHel 1996.39 822.85 4038.25
VTopHel 1836.37 822.85 4634.71
MBotHel 3236.19 20.58 -2548.72
Strength VBotHel 3329.01 20.58 -2893.18
Limit State MTopToe 1114.67 237.10 -305.31
VTopToe 1077.04 237.10 -427.61
MBotToe 2974.53 822.85 4212.08
VBotToe 3012.17 822.85 4334.39
MTopHel 2015.16 564.85 2492.79
Service MBotHel 2351.11 218.41 -971.61
Limit State MTopToe 2015.16 218.41 -971.61
MBotToe 2351.11 564.85 2492.79

The pile cap is designed for shear forces and bending moments calculated on the toe and
heel sides of the stem. The shear force is conservatively calculated at the face of the
stem rather than at a distance equal to the depth of the footing. For example, the shear
force at the heel side is calculated by reducing forces of the piles that are partially located
in the free body diagram, as well as considering other factored forces:

Vheel =
(pile reaction )(number of piles )( effective fraction of pile reaction )
footing length

−
(load factor )V1 − (load factor )V3 − (load factor ) LSVertical
footing length footing length footing length

−
(load factor )W1 (heel width ) / ( footing width )
footing length

=
(165.13 )(13 )( 0.928 ) − (1.35 )( 259.1) − (1.35 )( 6.1) − ( 0 )( 38.4 ) − (1.25 )( 240 )( 2.5 ) / (10 )
64 64 64 64 64
= 24.36 kip/ft

Pile reaction forces may be fractional depending on the pile's location with respect to the
heel's face. In this case, the center line of the second row of piles is located 8 ft from the
toe edge of the footing. The fraction of the pile reaction that contributes to the shear at
the heel is approximated as:

fraction ≈
(heel width ) − ( footing width-location of pile - pile diameter/2 )
pile diameter
2.5 − (10 − 8 − 1.167 / 2 )
≈ 0.928
=
1.167

The summary of the cap design forces per linear foot at the face of the stem (the toe side
and the heel side) are shown in Table 11.1.6-20.

11.1-40 Chapter 11.1 Abutments

© 2022 California Department of Transportation. ALL RIGHTS reserved.
 Bridge Design Practice 11.1 • October 2022

Table 11.1.6-20 Summary of Cap Design Forces per Liner Foot at the Face of Stem
(Toe Side and Heel Side)

Limit State Forces Top of Toe Bottom of Toe Top of Heel Bottom of Heel
Shear at face (kip/ft) 4.46 30.91 2.87 24.36
Strength
Moment at face (kip-ft/ft) 0.00 45.50 6.60 9.48
Service Moment at face (kip-ft/ft) 0.00 32.05 2.31 3.51

The steps for flexural design, shear design, crack control, and horizontal temperature
reinforcement of the pile cap are similar to the backwall or the stem wall.

11.1.6.9 Design Spread Footing

The backwall and stem wall design for the spread footing is the same as for the pile
foundation. The next portion of this example concentrates on the design of the same
abutment supported on a shallow foundation.
Table 11.1.6-21 provides the nominal bearing resistance (qn) and permissible net contact
stress (qpn) provided by GD based on the effective size of the footing. The contact stress
under the Service-I load combination is compared to qpn, and the bearing stresses under
Strength and Construction factored loads are compared to qR to meet design
requirements, where qR =φb qn.

Table 11.1.6-21 Nominal Bearing Resistance and Permissible

Net Contact Stress
Nominal bearing Resistance-qn Permissible net Stress-qpn
B′ (ft)
(ksf) (ksf)
4.0 26.96 17.8
5.0 29.12 16.3
6.0 31.28 14.8
7.0 33.44 13.3
8.0 35.57 12.2
9.0 37.67 11.3
10.0 39.72 10.5
11.0 41.73 9.9

Using governing load combinations and load factors reported by the CTAbut program (not
shown here), Table 11.1.6-22a and 11.1.6-22b summarize governing factored loads for
soil and structural checks, respectively of the abutment design.

Table 11.1.6-22a Summary of Governing Factored Loads for soil checks

Limit State Check Pu (kip) Vu (kip) Mu (kip-ft)
Bearing 1836.37 822.85 4634.71
Strength/Construction
Sliding 984.22 474.21 1240.67
Settlement 2351.11 564.85 2492.79
Service
Eccentricity 2015.16 564.85 2492.79

Chapter 11.1 Abutments 11.1-41

© 2022 California Department of Transportation. ALL RIGHTS reserved.
 Bridge Design Practice 11.1 • October 2022

Table 11.1.6-22b Summary of Factored Loads for structural check

P (axial load) V ( shear) M (moment)
Footing Sections
kip kip kip-ft
MTopHel 1996.39 822.85 4038.25
VTopHel 1996.39 822.85 4038.25
MBotHel 3236.19 20.58 2548.73
Strength VBotHel 3236.19 20.58 2548.73
Limit State MTopToe - - -
VTopToe - - -
MBotToe 2974.53 822.85 4212.08
VBotToe 2974.53 822.85 4212.08
MTopHel 2015.16 564.85 2492.79
Service MBotHel 2351.11 218.41 971.61
Limit State MTopToe - - -
MBotToe 2351.11 564.85 2492.79

11.1.6.9.1 Check Bearing Stresses

The first check for Strength/Construction load combinations is a bearing stress check.
The governing load combination is used to check the soil's bearing resistance and the
footing's size. Using absolute values of the moment and the axial force, the eccentricity,
effective footing width, and effective area are calculated as:

Mu 4634.71
=e = = 2.52 ft
Pg 1836.37

B=′ 10 − 2 ( 2.52 ) = 4.95 ft

=Ae (=
64 )( 4.95 ) 316.95 ft 2

The ultimate bearing stress is calculated based on a uniform stress distribution as the
footing is on soil:

1836.37
=
qg ,u = 5.79 ksf
316.95

The nominal bearing resistance qn is calculated from Table 11.1.6-21 using

B′ = 4.95 ft and interpolation between 26.96 ksf and 29.12 ksf as:

qn = 29.02 ksf

qR = φb qn = (0.45)(29.02) =13.06 ksf (AASHTO 10.6.3.1.1-1)

As qR > qg,u, the bearing stress is acceptable.

11.1-42 Chapter 11.1 Abutments

© 2022 California Department of Transportation. ALL RIGHTS reserved.
 Bridge Design Practice 11.1 • October 2022

11.1.6.9.2 Check Sliding

The second check for Strength/Construction load combinations is the sliding check.
Ignoring the backfill passive resistance, the factored sliding resistance is obtained by
Article 10.6.3.4 as:

RR =
φRn = 0.8P µ
φτR τ =

where P is the total vertical force, φτ is the resistance factor for sliding between soil and
foundation (AASHTO Table 10.5.5.2.2-1), and µ = tan (φf) where φf is the internal friction
angle of drained soil.

=RR 0.8
= ( 984.22 ) tan(34o ) 531.1 kip
Comparing the shear force effect of the footing to the factored shear resistance:

Vu = 474.21 kip < RR = 531.1 kip

Shear keys are not required herein to resist the sliding. In case shear keys are required,
the advantages and disadvantages of using shear keys should be considered in the
design. CTAbut provides the additional required shear force to design the shear key under
the footing in the full report only.

11.1.6.9.3 Check Settlements

The first check under the Service-I load combination is to compare the net uniform bearing
stress (qn,u) to the permissible net contact stress (qpn) to limit the settlement to the
permissible level. The axial load should be used as the net when calculating the bearing
stress for the settlement check. Using absolute values of the moment and the axial force,
the eccentricity, effective footing width, and effective area are calculated as:

Mn 2492.79
=e = = 1.06 ft
Pg 2351.11

10 − 2 (1.06 ) =
B′ = 7.88 ft

=Ae (=
64 )( 7.88 ) 504.32 ft 2

2351.11
=
qg ,u = 4.66 ksf
504.32
(
qg ,u − ( AverageOG − bottom of footing ) γ SE
qn,u = )
 120 
qn,u =  4.66 − ( 6.5 − 0 ) * 1.00 = 3.88 ksf
 1000 

Chapter 11.1 Abutments 11.1-43

© 2022 California Department of Transportation. ALL RIGHTS reserved.
 Bridge Design Practice 11.1 • October 2022

The permissible net contact stress qpn is calculated from Table 11.1.6-21 using B′ = 7.88
ft and interpolation between13.3 ksf and 12.2 ksf as:

qpn = 12.33 ksf

As qpn > qn,u, the contact bearing stress is acceptable.

11.1.6.9.4 Check Eccentricity

The second check under the Service-I load combination is the eccentricity check. The
gross axial force is used for this check. Therefore, the eccentricity is calculated as:

Mn 2492.79
=e = = 1.24 ft
Pg 2015.16

According to Article 10.5.2.2 (AASHTO-CA BDS-8), the maximum acceptable eccentricity

limit for footing on soil is:

Bftg/6 = 10/6 = 1.67 ft

The calculated eccentricity is less than the specified limit and is acceptable.

Note: If the footing is on the rock, the maximum eccentricity limit is Bftg/4.

11.1.6.9.5 Communicate with GD

Table 11.1.6-23 summarizes design loads to be provided by SD to GD during design.

Table 11.1.6-23a Design Loads to be provided by SD to GD

Mx (kip-ft) Vy (kip) P (gross) (kip)

Service Limit State
Mx_total Mx_perm Vy_total Vy_perm Ptotal Pperm
Mx_max 971.61 272.32 218.41 316.14 2351.11 1976.76
Mx_min 2492.79 272.32 564.85 316.14 2351.11 1976.76
Eccentricity
Pgrs_min 2492.79 272.32 564.85 316.14 2015.16 1976.76
Controlling Load 2492.79 272.32 564.85 316.14 2015.16 1976.76
Mx_max 971.61 272.32 218.41 316.14 2351.11 1976.76
Mx_min 2492.79 272.32 564.85 316.14 2351.11 1976.76
Settlement
Pnet_max 2492.79 272.32 564.85 316.14 2351.11 1976.76
Controlling Load 2492.79 272.32 564.85 316.14 2351.11 1976.76

Note – CTAbut reports Pgross in the soil check table. However, the settlement check
calculation must use Pnet.

11.1-44 Chapter 11.1 Abutments

© 2022 California Department of Transportation. ALL RIGHTS reserved.
 Bridge Design Practice 11.1 • October 2022

Table 11.1.6-23b Design Loads to be provided by SD to GD

Strength/Construction Mx Vy Ptotal(gross)
Limit States (kip-ft) (kip) (kip)
Mx_max 2893.18 20.58 3329.01
Mx_min 4634.71 822.85 2774.36
Bearing
Ptotal_max 2883.45 690.73 3366.65
Controlling Load 4634.71 822.85 1836.37
Vy_max 4634.71 822.85 2774.36
Vy_min 1072.58 0.00 2013.89
Sliding
Ptotal_min 1240.67 474.21 984.22
Controlling Load 1240.67 474.21 984.22

11.1.6.9.6 Design Strength

In order to calculate the internal forces of the footing, as shown in Figure 11.1.6-7, the
soil pressures, qleft (heel edge), qright (toe edge), q1 (at the face of the heel), and q2 (at the
face of the toe) are calculated. The following symbols are used:

M
P

2.5′ 4.0′ 3.5′ qright

q1 q2
qleft

Figure 11.1.6-7 Soil Pressures

Lftg = footing length (ft)

Mheel = moment at the face of the heel (kip-ft/ft)
Mheel_soil = moment due to the soil pressure at the face of the heel (kip-ft/ft)
Mtoe = moment at the face of the toe (kip-ft/ft)
Mtoe_soil = moment due to the soil pressure at the face of the toe (kip-ft/ft)
Vheel = shear at the face of the heel (kip/ft)
Vheel_soil = shear due to the soil pressure at the face of the heel (kip/ft)
Vtoe = shear at the face of the toe (kip/ft)

Chapter 11.1 Abutments 11.1-45

© 2022 California Department of Transportation. ALL RIGHTS reserved.
 Bridge Design Practice 11.1 • October 2022

Vtoe_soil = shear due to the soil pressure at the face of the toe (kip/ft)
Bftg = footing width (ft)
Wheel = heel width (ft)
Wtoe = toe length (ft)

The qleft and qright are calculated by the following equation

 qleft  P M
=  ±
qright 
2
Bftg Lftg Lftg Bftg /6

For example, for the case shown in Table 11.1.6-22b, the “MBotHel” forces are given as:
P = 3236.19 kip, and M = 2548.73 kip-ft.

Following is a summary of soil pressures calculations:

3236.19 2548.73
qleft = + =7.45ksf
(10)(64) (64)(10)2
6
3236.19 2548.73
qright = − =2.67 ksf
(10 )( 64 ) ( 64 )(10 )2
6

q1 =
qleft −
( )
qleft − qright Wheel
7.45 −
=
( 7.45 − 2.67 )( 2.5 ) =
6.25ksf
Wftg 10

q2 =
qright +
(
qleft − qright Wtoe )
2.67 +
=
( 7.45 − 2.67 )( 3.5 ) =
4.34 ksf
Wftg 10

Therefore, forces caused by the soil pressure are calculated as follows:

=Vheelsoil
(=
qleft + q1 )Wheel ( 7.45 + 6.25 )( 2.5 )
= 17.13 kip/ft
2 2

=
M
2
q1Wheel ( q − q1 )Wheel
+ left
2

heel soil
2 3
2 2
(
=
6.25 )( 2.5 )
+
( 7.45 − 6.25 )( 2.5 )
22.03 kip-ft/ft
=
2 3
For the structure design of the footing, the forces from the overburden soil and footing
need to be subtracted from the forces caused by the soil pressure, calculated above.

( LF )V1 + ( LF )V3 + ( LF ) LSVertical + ( LF )W1Wheel / Bftg

Vheel = Vheel _ soil −
Lftg

11.1-46 Chapter 11.1 Abutments

© 2022 California Department of Transportation. ALL RIGHTS reserved.
 Bridge Design Practice 11.1 • October 2022

 2.5 
(1.0)(259.1) + (1.0)(6.1) + (0)(38.4) + (1.25)(240)  
17.13 −
=  10  =11.81 kip/ft
64
( LF )V1 ( MA ) + ( LF )V3 ( MA ) + ( LF ) LSVertical ( MA ) + ( LF )W1 ( MA )Wheel / Bftg
=
Mheel Mheel _ soil −
Lftg
 2.5 
(1.0)(259.1)(1.25) + (1.0)(6.1)(1.25) + (0)(38.4)(1.25) + (1.25)(240)(1.25)  
22.03 −
=  10  =15.38 kip/ft
64
LF: Load Factor; MA: Moment Arm

After repeating the calculation for other sections of the footing a summary of the shear
and flexural footing design load effects was generated and shown in Table 11.1.6-24.

Table 11.1.6-24 Summary of the shear and flexural footing design loads
Limit State Forces Top Toe Bottom Toe Top Heel Bottom Heel
Shear at face (kip/ft) 0.00 21.93 6.69 11.81
Strength
Moment at face (kip-ft/ft) 0.00 41.20 8.98 15.38
Service Moment at face (kip-ft/ft) 0.00 28.24 3.35 6.75

The flexural and shear design steps for the footing are the same as for the pile foundation
or stem wall design. Therefore, it is not shown here.

Chapter 11.1 Abutments 11.1-47

© 2022 California Department of Transportation. ALL RIGHTS reserved.
 Bridge Design Practice 11.1 • October 2022

NOTATION
Ae = effective shear area of a cross-section (ft2)
As = total area of non-prestressed tension reinforcement (in.2)
a = depth of equivalent rectangular stress block (in.)
an = effective live load distribution width at the deck elevation (ft)
B’ = effective footing width (ft)
BOF = bottom of footing elevation (ft)
Bftg = tooting width (ft)
bn = effective live load distribution width at the top of the footing (ft)
bv = effective width of a member for shear stress calculations (in.)
C = correction factor for concrete-soil interference
Cgpile = center of gravity for pile group (ft)
c = distance from the extreme compression fiber to the neutral axis (in)
DCsup = dead load from superstructure (kip)
DCsub = dead load from substructure (kip)
DW = additional dead load from superstructure (kip)
d = distance from the face of footing to center of the pile (ft)
dbd = deformed bar diameter (in.)
dbw = backwall thickness (in. or ft)
dc = thickness of concrete cover measured from extreme tension fiber to center
of closest bar (in.)
de = effective depth from extreme compression fiber to the centroid of the tensile
force in the tensile reinforcement (in.)
dftg = footing thickness (ft)
dLS = depth of live load surcharge on heel (ft)
dv = effective shear depth (in.)
EH = horizontal earth pressure (kip)
LSH = horizontal live load surcharge (kip)
Ec = modulus of elasticity of concrete (ksi)
Es = modulus of elasticity of reinforcing steel (ksi)
e = eccentricity (ft)
f´c = specified 28-day compressive strength of unconfined concrete (ksi)
fr = modulus of rupture of concrete (ksi)

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© 2022 California Department of Transportation. ALL RIGHTS reserved.
 Bridge Design Practice 11.1 • October 2022

Fpile = horizontal reaction force of all batter piles (kip)

fss = tensile stress in mild steel at the service limit state (ksi)
fy = nominal yield stress for A706 reinforcing steel (ksi)
Fx = total maximum lateral load (kip)
h = abutment height (ft)
hbw = backwall height (ft)
I = moment of inertia
Icr = moment of inertia of the cracked cross-section of a member about its
centroidal axis (in.4)
Itr = moment of inertia of the transformed cross-section of a member about its
centroidal axis (in.4)
Ka = Coulomb’s active earth-pressure coefficient
Kp = Coulomb’s passive earth-pressure coefficient
k = ratio for transformed section
kde = effective depth from extreme compression fiber to the centroid of the tensile
force in the tensile reinforcement in transformed section (in)
Lftg = footing length (ft)
LLHL93 = design vehicular live load- HL-93 load (kip)
LLpermit = permit vehicular live load (kip)
Lr = permissible horizontal resistance of all piles (kip)
Mcr = cracking moment of a member’s cross-section (kip-ft)
Mn = nominal flexural resistance of a member’s cross-section (kip-ft)
Mr = factored flexural resistance of a section in bending (kip-ft)
Mu = factored moment at a section (kip-ft)
Ms = factored moment at a section for service limit state (kip-ft/ft)
MPF = multiple presence factor
N = equivalent number of lanes
n = modular ratio
nl = number of whole lanes that can be accommodated on the bridge
np = number of pile in each row
nmax = maximum number of design lanes that can be placed on the bridge
OG = original ground elevation (ft)
P = total vertical force (kip)

Chapter 11.1 Abutments 11.1-49

© 2022 California Department of Transportation. ALL RIGHTS reserved.
 Bridge Design Practice 11.1 • October 2022

PS = prestressing force at abutment (kip)

Pgross = factored axial force (kip)
Pnet = net effective load acting on the bottom of the footing (kip)
PPile = axial force of vertical pile (kip)
Pu = factored axial force (kip)
qg,u = gross uniform bearing stress (ksf)
qn = nominal bearing resistance (ksf)
qn,u = net uniform bearing stress (ksf)
qpn = permissible net stress (ksf)
qR = factored bearing resistance (ksf)
Rτ = nominal sliding resistance against failure by sliding (kip)
RR = factored resistance force against failure by sliding (kip)
Rτ = nominal sliding resistance between soil and foundation (kip)
s = spacing of reinforcing bars (in.)
Vc = nominal shear strength provided by concrete (kip)
Vn = nominal shear strength of a section (kip)
Vp = component of the prestressing force in the direction of applied shear (kip)
Vpad = bearing pad shear (kip)
Vs = nominal shear strength provided by shear reinforcement (kip)
W = abutment length along the skew (ft)
β = factor indicating ability to diagonally cracked concrete to transmit tension
and shear (AASHTO 5.7.3.4.1)
β1 = stress block factor taken as the ratio of the depth of the equivalent uniformly
stressed compression zone assumed in the strength limit state to the depth
of the actual compression zone
βs = ratio of flexural strain at the extreme tension face to the strain at the centroid
of the reinforcement layer nearest the tension face
εs = strain in the centroid of the tension reinforcement (in/in)
φ = angle of internal friction; strength reduction factor
φb = resistance factor for bearing of shallow foundation
φf = internal friction angle
φ𝜏𝜏 = resistance factor for shear resistance between soil and foundation specified
in Table 10.5.5.2.2-1
γ1 = flexural cracking variability factor (AASHTO 5.6.3.3)

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© 2022 California Department of Transportation. ALL RIGHTS reserved.
 Bridge Design Practice 11.1 • October 2022

γ3 = ratio of specified minimum yield strength to ultimate tensile strength of the

non-prestressed reinforcement (AASHTO 5.6.3.3)
γc = weight of the concrete per unit volume (pcf)
gs = weight of the soil per unit volume (pcf)
γe = crack control exposure factor (AASHTO 5.6.7)
θ = angle of the load distribution (degree)
θsk = skew angle
ρ = ratio of volume of reinforcement to the concrete volume confined by the
reinforcement

Chapter 11.1 Abutments 11.1-51

© 2022 California Department of Transportation. ALL RIGHTS reserved.
 Bridge Design Practice 11.1 • October 2022

REFERENCES
1. AASHTO. (2017). AASHTO LRFD Bridge Design Specifications, 8th Edition,
American Association of State Highway and Transportation Officials, Washington
DC.
2. Caltrans. (2019a). California Amendments to AASHTO LRFD Bridge Design
Specifications, 8th Edition, California Department of Transportation, Sacramento,
3. CA.Caltrans. (2019b). Caltrans Seismic Design Criteria, Version 2.0, California
Department of Transportation, Sacramento, CA.
4. Caltrans. (2019c). CTBridge Program, Version 1.8.3 California Department of
Transportation, Sacramento, CA.
5. Caltrans. (2020). Bridge Design Details, Chapter 6, California Department of
Transportation, Sacramento, CA.
6. Caltrans. (2022). CT- Abut program, Version 3.1.0, California Department of
Transportation, Sacramento, CA.
7. Zokaie, T., Malek, A., and Rahbari, A. (2015). “Live Load Distribution on Bridge
Abutments,” Western Bridge Engineers Seminar, September 9-11, Reno, NV.

11.1-52 Chapter 11.1 Abutments

© 2022 California Department of Transportation. ALL RIGHTS reserved.