1

1 INTRODUCTION

1.0 General

The LRFD design procedure for conventional gravity and cantilever retaining walls,

abutments and MSE walls, with a few exceptions, is identical to the ASD design procedure

utilized in the past. Generally, ultimate bearing capacity, resistance to sliding, overall stability,

wall foundation settlement, and lateral deflection limits are checked. Total as well as

differential settlements are major criteria for determining wall type. See excerpts in Appendix

C taken from FDOT’s Plans Preparation Manual – Volume I showing wall type selection

criteria based on anticipated settlement and the environmental classification of the site.

Therefore, the first step of a retaining wall design is to calculate the settlements based on the

fill heights.

1.1 Design Summary

In ASD design, all the uncertainties in the applied loads and ultimate geotechnical or

structural capacity are factored in safety factors or allowable stresses. Whereas, LRFD

separates the variability of these design components and resistance factors to the load and

material capacity, respectively. The key issues in the design of retaining walls and abutments

by LRFD is the application of maximum and minimum load factors for dead , earth and

surcharge loads. See Table 1 and Figures 1 through 3 below.

1.1.1 Dead or Permanent Loads

DC = dead load of structural component and nonstructural attachments (for conventional retaining walls not for MSE Walls)

DW = dead load for wearing surfaces and utilities EH = horizontal earth pressure load ES = earth surcharge load EV = vertical pressure from dead load of earth fill

1.1.2 Live or Transient Loads

LS = live load surcharge WA = water load and stream pressure

2

Table 3.4.1-1 Load Combinations and Load Factors.

Use One of These at a Time Load Combination

Limit State

DC DD DW EH EV ES EL

LL IM CE BR PL LS WA WS WL FR

TU CR SH TG SE EQ IC CT CV

STRENGTH I (unless noted)

γp 1.75 1.00 — — 1.00 0.50/1.20 γTG γSE — — — —

STRENGTH II γp 1.35 1.00 — — 1.00 0.50/1.20 γTG γSE — — — — STRENGTH III γp — 1.00 1.40 — 1.00 0.50/1.20 γTG γSE — — — — STRENGTH IV γp — 1.00 — — 1.00 0.50/1.20 — — — — — — STRENGTH V γp 1.35 1.00 0.40 1.0 1.00 0.50/1.20 γTG γSE — — — — EXTREME EVENT I

γp γEQ 1.00 — — 1.00 — — — 1.00 — — —

EXTREME EVENT II

γp 0.50 1.00 — — 1.00 — — — — 1.00 1.00 1.00

SERVICE I 1.00 1.00 1.00 0.30 1.0 1.00 1.00/1.20 γTG γSE — — — — 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 γTG γSE — — — —

SERVICE IV 1.00 — 1.00 0.70 — 1.00 1.00/1.20 — 1.0 — — — —

FATIGUE—LL, IM & CE ONLY

— 0.75 — — — — — — — — — — —

Table 3.4.1-2 Load Factors for Permanent Loads, γp.

Load Factor Type of Load, Foundation Type, and Method Used to Calculate Downdrag Maximum Minimum

DC: Component and Attachments DC: Strength IV only

1.25 1.50

0.90 0.90

DD: Downdrag Piles, α Τοmlinson Method Piles, λ Method Drilled shafts, O’Neil and Reese (1999) Method

1.40 1.05 1.25

0.25 0.30 0.35

DW: Wearing Surfaces and Utilities 1.50 0.65 EH: Horizontal Earth Pressure

• Active • At-Rest

1.50 1.35

0.90 0.90

EL: Locked-in Erection Stresses 1.00 1.00 EV: Vertical Earth Pressure

• Overall Stability • Retaining Walls and Abutments • Rigid Buried Structure • Rigid Frames • Flexible Buried Structures other than Metal Box Culverts • Flexible Metal Box Culverts

1.00 1.35 1.30 1.35 1.95 1.50

N/A 1.00 0.90 0.90 0.90 0.90

ES: Earth Surcharge 1.50 0.75

3

1.1.3 Typical Application of Load Factors

a. Dead or permanent load

Figure 1 - Bearing resistance for both

conventional and MSE walls

Figure 2 - Sliding and Eccentricity for

conventional and MSE walls

Figure 3 - Live or transient loads

4

2.0 Conventional Retaining Walls 2.1 Overall Stability

Investigate Service 1 load combination using an appropriate resistance factor. In

general, the resistance factor, φ, may be taken as;

• 0.75 - where the geotechnical parameters are well defined, and slope does not

support or contain a structural element.

• 0.65 – where the geotechnical parameters are based on limited information or the

slope contains or supports a structural element.

2.2 Bearing Resistance

Investigate bearing resistance at the strength limit state using appropriate factored

loads and resistances as described below.

2.2.1 Wall Supported on Soils

The vertical stress shall be calculated assuming a uniformly distributed

pressure over an effective base area.

eBV

v 2−Σ

=σ (11.6.3.2-1)

Figure 4

5

2.2.2 Wall Supported on Rocks

If the resultant force is within the middle third of the base;

)61(max Be

BV

V +Σ

=σ (11.6.3.2-2)

)61(min Be

BV

V −Σ

=σ (11.6.3.2-3)

If the resultant force is outside of the middle third

of the base;

])2[(32

max eBV

V−

Σ=σ (11.6.3.2-4)

0min =Vσ (11.6.3.2-5)

Figure 5

2.2.3 Soil Bearing Resistance

nbR qq φ= (10.6.3.1.1-1)

γγγγ wmwqqmfcmn CBNgCNDgcNq 5.0++= (10.6.3.1.2a-1)

Where: g = gravitational acceleration (ft/sec2)

c = cohesion

Ncm = Ncscic, bearing capacity factor for cohesion

Nqm = Nqsqdqiq , surcharge bearing capacity factor

Nγm = Nγsγiγ, unit weight bearing capacity factor

γ = total (moist) unit weight of soil above or below the bearing depth of the

footing.

Df = footing embedment depth (ft)

B = footing width (ft)

Cwq,Cwγ= correction factors for water table

sc,sγ,sq = footing shape correction factors

dq = correction factor for shear resistance along the failure surface passing

through cohesionless materials above the bearing elevation.

ic,iγ,iq = load inclination factors

Figure 5

6

n

fq cBLV

Hi⎥⎥⎦

⎤

⎢⎢⎣

⎡

+−=

φcot1 (10.6.3.1.2a-7)

1

cot1

+

⎥⎥⎦

⎤

⎢⎢⎣

⎡

+−=

n

fcBLVHi

φγ (10.6.3.1.2a-8)

θθ 22 sin1

2cos

1

2

⎥⎥⎦

⎤

⎢⎢⎣

⎡

+

++

⎥⎥⎦

⎤

⎢⎢⎣

⎡

+

+=

LB

LB

BL

BL

n (10.6.3.1.2a-9)

All these factors can be found in Article 10.6.3.1.2 of the Interim AASHTO 2006 LRFD

Specifications.

2.3 Overturning or Eccentricity (Article 11.6.3.3)

For foundations on soil, the resultant of the reaction pressure distribution shall be

located within the middle one-half of the base width.

For foundations on rock, the resultant of the reaction pressure distribution shall be

located within the middle three-fourths of the base width.

2.4 Sliding

Check spread footing against sliding in accordance with the provisions of Article

10.6.3.4. Passive resistance of soil in front of walls used in stability computation shall be

carefully evaluated accounting for possible future excavations, either temporary or permanent,

and/or long term erosion, etc.

For clayey soils beneath the footing, QR, against failure by sliding is:

RR = φτR τ + φep Rep (11.6.3.4-1)

where:

φτ = Resistant factor for shear resistance between soil and foundation specified in

Table 10.5.5.2.2-1

Rτ= Nominal shear resistance between footing and foundation material (ton); and

Rep= Nominal passive resistance of foundation material available throughout the

design life of the footing (ton). [ pp2

p K H c 2 K H ½ P += γ ]

φep = 0.5, Table 10.5.5.2.2-1

If the soil beneath the footing is cohesionless, then:

7

Rτ= V*tan δ (11.6.3.4-2)

in which: tan δ = tan φf for concrete cast against soil,

= 0.8 tan φf for precast concrete footing (φ = 0.8 from Table 3, page 26)

V = total vertical force (tons)

φf = the internal friction angle of soil (o)

Example Problem 1:

Foundation soil properties:

γ2 = 110 pcf γ2’= 58 pcf φ2 = 33o

LS = 250 psf

The cantilever retaining wall is being considered for a grade separation between roadway

lanes in a non-seismic area. The wall will be backfilled with a free draining granular fill such

that the seasonal high water table will be below the bottom of the footing. The vehicular live

load surcharge, LS, on the backfill will be applied as shown in the figure.

Approach: To perform the evaluation, the following steps are taken:

The loads and resulting moments due to structure components, earth pressures and live

load surcharge are calculated; and

The appropriate load factors and combinations are determined and multiplied by the

unfactored loads and moments to determine the factored loading conditions.

Step 1: Calculate the Unfactored Loads

(A) Dead Load of Structural Components and Nonstructural Attachments (DC)

Figure 6

8

Assuming a unit weight of concrete, γc, equal to 150 pcf, W1 = B1 H1 γc =1’x15’x0.150 =2.25 kips/ft W2 = 0.5 B2 H1 γc=0.5x0.5’x15’x0.150=0.562 kips/ft W3 = B H2 γc = 9.5’x1.5’x0.150=2.14 kips/ft

(B) Vertical Earth Pressure (EV)

Unit Weight of Soil γ1 = 105 pcf

Weight of Soil on Footing

PEV = W4 = B3H1γ1 = 6.5’ x 15’ x 105= 10.24 kips/ft

(C ) Live Load Surcharge (LS)

A live load surcharge is applied when vehicle loads will be supported on the backfill within a

distance equal to H. The unit vertical component of LS is:

For a heel width B3 of 6.5’:

length wallof ftkips = )psf)(( = B p = P 3LSVLSV /625.1'5.6250

The active earth pressure coefficient ka for a wall friction angle, δ = 0 and a horizontal back

slope is:

k = ka = 0.33

ftpsfLS k = p /5.8225033.0 =×=Δ

Using a rectangular distribution, the live load horizontal earth pressure acting on the wall is:

length wallof ftkips = )psf)(( = H p = PLSH /36.1'5.165.82Δ

(D) Horizontal Earth Pressure (EH)

The lateral earth pressure is assumed to vary linearly with the depth of soil backfill as

given by:

p = kγ'z where k = 0.33

At the base of the footing (i.e., @ z = H):

p = (0.333) (105) (16.5’) = 577 psf

The horizontal earth pressure (triangular distribution) acting on the wall is:

PEH = ½ pH = (0.5) (577) (16.5’) = 4.76 kips/ft length of wall

Figure 7

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(E) Summary of Unfactored Loads

Unfactored Vertical Loads and Resisting Moments

Item

V

(kips/ft)

Moment Arm About Toe (ft)

Moment About Toe (kip-ft/ft)

W1

2.25 2.5 5.625

W2

0.56 1.83 1.03

W3

2.14 4.75 10.165

PEV 10.24 6.25 64.00

PLSV 1.63 6.25 10.188

TOTAL 16.82

Unfactored Horizontal Loads and Overturning Moments

Item

H

(kip/ft)

Moment Arm About Toe (ft)

Moment About Toe (kip-ft/ft)

PLSH

1.36

8.25

11.22

PEH

4.76

5.5

26.18

Step 2: Determine the Appropriate Load Factors

In theory, structures could be evaluated for each of the limit states. However, depending on

the particular loading conditions and performance characteristics of a structure, only certain

controlling limit states need to be evaluated. For the example problem, each limit state will

be qualitatively assessed below relative to that limit state is applicable for the design problem:

• Strength I - Basic load combination related to the normal vehicular use of the bridge

without wind. (Applicable as a standard load case).

• Strength II - Load combination relating to the use of the bridge by Owner specified

special design vehicles and/or evaluation permit vehicles, without wind. (Not

10

applicable because special vehicle loading is not specified).

• Strength III - Load combination relating to the bridge exposed to wind velocity

exceeding 55 mph without live loads. (Not applicable because wall is not subjected to

other than standard wind loading).

• Strength IV - Load combination relating to very high dead load to live load force

effect ratios exceeding about 7.0 (e.g., for spans greater than 250 feet). (Applicable

because dead loads predominate).

• Strength V - Load combination relating to normal vehicular use of the bridge with

wind velocity of 55 mph (Not applicable because wind load not a design

consideration).

• Extreme Event I - Load combination including earthquake. (Not applicable because

problem does not include earthquake loading).

• Extreme Event II - Load combination relating to ice load or collision by vessels and

vehicles. (Not applicable because problem does not include ice or collision loading).

• Service I - Load combination relating to the normal operational use of the bridge with

55 mph wind. (Applicable for design loading).

• Service II - Load Combination intended to control yielding of steel structures and slip

of slip-critical connections due to vehicular live load. (Not applicable due to structure

type).

• Service III - Load combination relating only to tension in prestressed concrete

structures with the objective of crack control. (Not applicable due to structure type).

• Fatigue - Fatigue and fracture load combination relating to repetitive gravitational

vehicular live load and dynamic responses under a single design truck. (Not applicable

due to structure type).

Consequently, the applicable load factors and combinations the example problem are

summarized in the following tables. From the descriptions above, it is apparent that only the

Strength I, Strength IV and Service I Limit States apply to the retaining wall design. Strength

I-a and I-b represent the Strength I Limit State using maximum and minimum load factors,

respectively,

Load Factors

11

Group

DC

EV

LSv

LSH

EH

(active)

Probable USE

Strength I-a

0.90

1.00

1.75

1.75

1.50

BC/EC/SL

Strength I-b

1.25

1.35

1.75

1.75

1.50

BC (max. value)

Strength IV

1.50

1.35

-

-

1.50

BC (max. value)

Service I

1.00

1.00

1.00

1.00

1.00

Settlement

Notes: BC - Bearing Capacity; EC - Eccentricity; SL - Sliding

By inspection:

• Strength I-a (minimum vertical loads and maximum horizontal loads) will govern for

the case of sliding and eccentricity (overturning); and

• For the case of bearing capacity, maximum vertical loads will govern, and the factored

loads must be compared for Strength I-b and Strength IV.

Step 3: Calculate the Factored Loads and Factored Moments

Factored Vertical Loads

Group/

Item Units

W1

Kips/ft

W2

Kips/ft

W3

Kips/ft

PEV

Kips/ft

PLSV

Kips/ft

Total

Kips/ft V (Unf.) 2.25 0.56 2.14 10.24 1.63 16.82

Strength I-a 2.03 0.50 1.93 10.24 2.85 17.55

Strength I-b 2.81 0.70 2.68 13.82 2.85 22.86

Strength IV 3.38 0.84 3.21 13.82 - 21.25

Service I 2.25 0.56 2.14 10.24 1.63 16.82

Factored Horizontal Loads

12

Group/Item Units

PLSH Kips/ft

PEH Kips/ft

Total Kips/ft

H (Unf.) 1.36 4.76 6.12

Strength I-a 2.38 7.14 9.52

Strength I-b 2.38 7.14 9.52

Strength IV - 7.14 7.14

Service I 1.36 4.76 6.12

Factored Moments from Vertical Forces (Mv)

Group/Item

Units

W1

Kip-ft/ft

W2

Kip-ft/ft

W3

Kip-ft/ft

PEV

Kip-ft/ft

PLSV

Kip-ft/ft

Total

Kip-ft/ft Mv (Unf.) 5.63 1.03 10.17 64 10.19 91.01

Strength I-a 5.06 0.93 9.15 64 17.83 96.97

Strength I-b 7.04 1.29 12.71 86.40 17.83 125.25

Strength IV 8.45 1.55 15.25 86.40 --- 111.63

Service I 5.63 1.03 10.17 64 10.19 91.01

Factored Moments from Horizontal Forces (Mh)

Group/Item

Units

PLSH

Kip-ft/ft

PEH

Kip-ft/ft

Total

Kip-ft/ft Mh (Unf.) 11.23 26.18 37.41

Strength I-a 19.65 39.27 58.92

Strength I-b 19.65 39.27 58.92

Strength IV - 39.27 39.27

Service I 11.23 26.18 37.41

Step 4 Stability Analyses

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a. Overturning or Eccentricity

e = B/2 -Xo B/2 =9.5 / 2 = 4.75’

Xo = (MVdl - MHtotal) / Vdl

emax = B/4 = 9.5 / 4 = 2.375’

Group/Item

Units

Vdl.

Kip /ft

Htotal

Kip /ft

MVdl

Kip-ft/ft

MHtotal

Kip-ft/ft

Xo Ft

e ft

emax Ft

Strength I-a

14.70 9.52 79.14 58.92 1.38 3.37 2.375

Strength I-b

20.01 9.52 107.43 58.92 2.42 2.33 2.375

Strength IV

21.25 7.14 111.63 39.27 3.41 1.34 2.375

Service I

15.19 6.12 80.82 37.41 2.86 1.89 2.375

For load case Strength 1-a, e is greater than emax , therefore, the design revised regard to

eccentricity.

b. Bearing Resistance

The adequacy for bearing resistance is based on a rectangular distribution of soil pressure

over the reduced effective area. For a rectangular distribution:

L’ = 1 foot (unit length of wall)

B’ = B – 2e

eB

VV 2−

Σ=σ (11.6.3.2-1)

MVtotal MHtotal X0 CDR

14

Group/Item Units

ΣV Kip /ft

Kips-ft/ft Kips-ft/ft e ft

B’ ft

σ ksf

Strength I-a 17.55 96.97 58.92 2.17 2.58 4.34 4.05 1.58

Strength I-b 22.86 125.25 58.92 2.90 1.85 5.80 3.94 1.62

Strength IV 21.25 111.63 39.27 3.41 1.34 6.81 3.12 2.05

Service I 16.82 91.01 37.41 3.19 1.56 6.31 2.64 2.42

Bearing resistance of soil

nbR qq φ= (10.6.3.1.1-1)

γγγγ wmwqqmfcmn CBNgCNDgcNq 5.0++= (10.6.3.1.2a-1)

c = 0, φ = 33o, γ2 = 110 pcf, and γ2’ = 58 pcf

Nq = 26.1, N γ = 35.2 [Table 10.6.3.1.2a-1]

Cwq= 1 (Dw = Df) [Table 10.6.3.1.2a-2]

Cw γ = 0.5

sq = 1 + (B/L)tanφf =1 (L>>B) [Table 10.6.3.1.2a-3]

sγ = 1 - 0.4(B/L) =1 [Table 10.6.3.1.2a-3]

dq = 1 [Table 10.6.3.1.2a-4]

For modest embedment of footing, it is usually to omission of the inclination factors.

Nqm = Nqsqdqiq=26.1x1x1x1=26.1

N γm = N γsγiγ=35.2x1x1=35.2

5.02.3534.4110.05.011.263110.0 ××××+×××=nq = 12.8 ksf/ft

qR = Фqn, use Ф= 0.5

qR = 0.5x12.8=6.4 ksf/ft

qR > σ in all loading cases , therefore, the footing design is adequate.

c. Check sliding

δφττ tan××= VR where: 8.0tantan

)9.0(

=

=+×=

τφ

φδ f

EVDCV

τR = 0.8 (17.55-2.85) (tan 33o) = 7.63 kips/ft < Htotal in load cases strength Ia & Ib.

15

Figure 8

The design has to be modified by either adding a key or lengthening the footing width.

3.0 Mechanically Stabilized Earth

(MSE) Walls Mechanically stabilized earth (MSE)

walls are composed of a reinforced soil

mass/volume, and a discrete modular

precast concrete facing which is vertical or

near vertical. The reinforced soil mass

consists of selected backfill. The tensile

reinforcements may be proprietary, and may

employ either metallic (i.e., strip or

mesh/grid-typed) or polymeric grid. Figure

8 shows the typical MSE wall configuration,

which is reproduced from the AASHTO

Specifications Figure 11.10.2-1.

MSE walls may be used where conventional gravity, cantilever, or counterfort

retaining walls are considered. They can accommodate larger total and differential

settlements than conventional gravity, cantilever, or counterfort retaining walls. However

there are some design limitations related to the rigid facing elements related to very high total

and differential settlement applications resulting in the need for two-phased construction

solutions.

MSE walls shall not be used in the following site conditions: (1) where utilities are to

be constructed within the reinforced soil mass; (2) where floodplain erosion or scour may

undermine the foundation support; and (3) in the case of steel reinforcements , where exposed

to surface or groundwater contaminated by acid mine drainage, industrial pollutants,

fertilizers or other aggressive environment that will cost long-term corrosions, (4) constructed

over existing storm sewer systems unless attention is given to including possible joint leakage

countermeasures.

16

Figure 9

The size of the reinforced soil mass is

based on consideration of external stability of

the system, geotechnical resistance, the

structural resistance within the reinforced soil

mass and panel units. The minimum soil

reinforcement length required for external

stability should be in accord with the FDOT’s

Structures Design Guidelines Section 3.13.2

in lieu of AASHTO Specifications 11.10.2.1.

The minimum required reinforcement length

for various conditions is as follows;

Walls in front of abutment on piling

L ≥ 8 feet and

L ≥ 0.7H1

Walls supporting abutment on spread footings

L ≥ 22 feet and

L ≥ 0.6(H1 + d) + 6.5 feet and

L ≥ 0.7H1

Where: H1 = mechanical height of wall and measured to the point

where potential failure plan intersects slope backfill

face, in feet.

L = reinforcement length required for external stability, in

feet.

d =fill height above wall

Reinforcement length shall be increased as required for surcharges and other external loads,

or for soft/weak foundation soils. Regardless of wall height, the minimum reinforcement

length shall be eight (8) feet.

3.1 Minimum Front Face Embedment

The AASHTO requirements for the minimum front face embedment are outlined in

Article 11.10.2.2. In addition to this FDOT’s Structures Design Guidelines also have the

following requirements;

17 Figure 10

1. Consider scour and bearing capacity when determining front face embedment depth;

2. Consult the District Drainage and Geotechnical Engineers to determine the elevation

of the top of leveling pad; and

3. The minimum front face embedment at a slope

should comply with Figure 9.

3.2 Other MSE Wall Design Issues Requirements according to the FDOT Structures

Design Guideline (Section 3.13.2)

A. Concrete Class and Cover

Table 2 (SDG Table 3.13.2.A)

Distance (D) from wall to a body of water with high chloride

content (≥ 2000 ppm) or any coal burning industrial facility,

pulpwood plant, fertilizer plant or similar industries

Concrete

Type

Concrete

Cover,

inches

D > 2,500 feet (low air contaminants) Class II 2

2,500 feet ≥ D ≥ 300 feet (moderate air contaminants) Class IV 2

D < 300 feet (extreme air contaminants) Class IV 3

B. Service Life

a. Permanent wall – 75 years

b. Abutment walls on spread

footings – 100 years

c. Temporary walls – for the length

of contract or three (3) years,

whichever is greater.

C. Acute Corner Walls (see Figure 10)

a. Define as two wall intersect at an angle

less than 70o ;

b. Design the acute nose wall as at-rest bin;

c. The bin should design with slip joints to

tolerate differential settlements from the

remainder of the structures;

d. The nose bin wall should be considered

18

Figure 11

as a facing element restrained by proper soil reinforcements; and

e. Design of facing connections, pullout and strength of reinforcing elements and

obstructions must conform to the general requirements of MSE wall design.

3.3 Stability Analyses

In LRFD analyses, it separates the

variability of the design components by applying

load and resistance factors to the load and material

capacity, respectively, similar to the conventional

retaining wall analyses.

3.3.1 Overall Stability (Article 11.10.4.3)

The provision of Article 11.6.2.3 shall apply.

Overall and compound stability of complex MSE

wall system shall also be investigated, especially

where the wall is located on sloping or soft ground where overall

stability may be inadequate. The long term strength of each backfill reinforcement layer

intersected by the failure surface should be considered as restoring forces in the limit

equilibrium slope stability analysis.

3.3.2 External Stability Analyses

The engineering properties of the retained soil mass used for MSE wall design

according to the FDOT’s Structures Design Guidelines, Section 3.13.12.G shall be

(1) Sand Backfill - friction angle, φ , of 30o, and unit weight, γ, of 105 pcf;

(2) Limerock backfill (in Dade and Monroe Counties), friction angle, φ , of 34o, and unit

weight, γ, of 115 pcf.

(3) Traffic surcharge present and locate within 0.5H1 of the back of the reinforced soil

volume should be included in the analysis.

(4) The Geotechnical Engineer of Record for the project is responsible for the external

stability analyses and design of the soil reinforcement length based on the analysis.

In performing the external stability analyses, engineers should assume the reinforced fill

19

volume as a rigid body similar to that of a gravity wall, which shall satisfy eccentricity,

sliding and bearing resistance criteria.

3.3.2.1 Overturning or Eccentricity

The provisions of Article 11.6.3.3 shall apply.

3.3.2.2 Sliding

The provisions of Article 10.6.3.3 shall apply. The coefficient of friction angle shall be

determined as;

• For discontinuous reinforcements, such as strips – the lesser of friction angle of either

reinforced backfill, φr, or foundation soil, φf;

• For continuous reinforcements, such as grids and sheets – the lesser of φr, φf, and ρ,

where ρ is the soil-reinforcement interface friction angle and a value of 2/3 φf may be

used. Other FDOT Structures Design Guideline Issues (Section 3.13.2)

3.3.2.3 Bearing Resistance

Effective width will be used to account for the effects of eccentricity as well as

inclination, B’=L-2e. Uniform bearing pressure shall be computed over the effective width.

nbR qq φ= (10.6.3.1.1-1)

γγγγ wmwqqmfcmn CBNgCNDgcNq 5.0++= (10.6.3.1.2a-1)

Where: Ncm = Ncscdcic

Nqm = Nqsqdqiq

N γm = N γsγiγ

Nc, Nq , N γ = bearing capacity factors

Cwq, Cw γ = correction factors to account for the location of the water table

g = gravitational acceleration (ft/sec2)

γ = total (moist) unit weight of soil above or below the bearing depth

Df = footing embedment depth (ft)

sq = 1 + (B/L)tanφf =1 (L>>B) [Table 10.6.3.1.2a-3]

sγ = 1 - 0.4(B/L) =1 [Table 10.6.3.1.2a-3]

dq = correction factor to account for the shearing resistance along the

failure surface passing through cohesionless material above the

bearing elevation [Table 10.6.3.1.2a-4]

20

D

Design Example 2a – MSE Wall External

Stability

Wall height

H = 20 feet, D = 2

Reinforced soil mass:

φr = 30o

γr = 105 pcf

Retained fill:

φf = 30o

γf = 105 pcf

Foundation soils: Figure 12 - MSE Example

φF = 30o

γF = 105 pcf (total/moist)

Traffic/live loads:

q = 250 psf/ft

ka = tan2(45 – φ/2) = 0.333

L = 14 feet (if the wall facing panels are thick, L will used and weight of panels should be

calculated as dead load, W)

Step 1 Calculate the unfactored loads

Vertical earth load of reinforced soil mass:

PEV = V1 = γr HL = 105 x 20 x 14 = 29,400 #/ft or 29.4 kips/ft

PLSV = q L = 250 x 14 = 3,500 #/ft or 3.5 kips/ft

PEH = F1 = 0.5 γf H2 ka = 0.5 x 105 x (20)2 x 0.3333 = 6,999 #/ft or 7 kips/ft

PLSH = F2 = qH ka = 250 x 20 x 0.3333 = 1,667 #/ft or 1.67 kips/ft

21

Unfactored Vertical Loads and Resisting Moments

Item

V

(kips/ft)

Moment Arm About Toe (ft)

Moment About Toe

(kip-ft/ft)

PEV 29.4 7.0 205.8

PLSV 3.5 7.0 24.5

TOTAL 32.9

Unfactored Horizontal Loads and Overturning Moments

Item

H

(kip/ft)

Moment Arm About Toe (ft)

Moment About Toe (kip-ft/ft)

PLSH

1.67

10.0

16.7

PEH

7

6.7

46.7

Step 2 Determine the appropriate load factors

Load Factors

Group

DC

EV

LSv

LSH

EH (active)

Probable USE

Strength I-a

0.90

1.00

1.75

1.75

1.50

BC/EC/SL

Strength I-b

1.25

1.35

1.75

1.75

1.50

BC (max. value)

Service I

1.00

1.00

1.00

1.00

1.00

Settlement

Notes: BC - Bearing Capacity; EC - Eccentricity; SL - Sliding

Step 3: Calculate the Factored Loads and Factored Moments

22

Factored Vertical Loads

Group/

Item Units

PEV

Kips/ft

PLSV

Kips/ft

Total

Kips/ft V (Unf.) 29.4 3.5 32.9

Strength I-a 29.4 6.13 35.5

Strength I-b 39.7 6.13 45.8

Service I 29.4 3.5 32.9

Factored Horizontal Loads

Group/Item

Units

PLSH

Kips/ft

PEH

Kips/ft

Total

Kips/ft H (Unf.) 1.67 7 8.7

Strength I-a 2.98 10.49 13.5

Strength I-b 2.98 10.49 13.5

Service I 1.67 7 8.7

Factored Moments from Vertical Forces (Mv)

Group/Item

Units

PEV

Kip-ft/ft

PLSV

Kip-ft/ft

Total

Kip-ft/ft Mv (Unf.)

205.8 24.5 230.3

Strength I-a

205.8 42.9 248.7

Strength I-b

277.8 42.9 320.7

Service I

205.8 24.5 230.3

23

Factored Moments from Horizontal Forces (Mh)

Group/Item

Units

PLSH

Kip-ft/ft

PEH

Kip-ft/ft

Total

Kip-ft/ft Mh (Unf.)

16.7 46.7 63.4

Strength I-a

29.23 69.93 99.16

Strength I-b

29.23 69.93 99.16

Service I

16.7 46.7 63.4

Step 4 Stability Analyses

a. Overturning or Eccentricity

e = B/2 -Xo B/2 =14 / 2 = 7’

Xo = (MV. Dead Load - MHtotal) / VDead Load

emax = B/4 = 14 / 4 = 3.5’

Group/Item

Units

VD.L.

Kip /ft

Htotal

Kip /ft

MV.D.L.

Kip-ft/ft

MHtotal

Kip-ft/ft

Xo ft

e ft

emax ft

CDR

Strength I-a 29.4 13.5 205.8 99.16 3.63 3.37 3.5 0.96

Strength I-b 39.7 13.5 277.8 99.16 4.49 2.51 3.5 0.72

Service I 29.4 8.7 205.8 63.4 4.84 2.16 3.5 0.62

In all loading cases, e < emax (or CDR < 1), thus the design is adequate with regard to

eccentricity.

b. Bearing resistance

B’ = B – 2e

eB

VV 2−

Σ=σ

Eccentricity to calculate reduced footing area:

e2 = B/2 -Xo B/2 =14 / 2 = 7’

Xo = (MV total - MHtotal) / Vtotal

24

emax = B/4 = 14 / 4 = 3.5’

Group/Item Units

Vtotal

Kip /ft

Htotal

Kip /ft

MVtotal

Kip-ft/ft

MHtotal

Kip-ft/ft

Xo ft

e2 ft

ema

x ft

B’ ft

qR σv

Ksf/ft CDR

Strength I-a 35.5 13.5 248.7 99.16 4.21 2.78 3.5 8.44 4.85 4.21 1.15

Strength I-b 45.8 13.5 320.7 99.16 4.83 2.16 3.5 9.68 5.25 4.73 1.11

Service I 32.9 8.7 230.3 63.4 5.07 1.92 3.5 10.1

6 5.41 3.24 1.67

CDR is > 1.0 in all cases; therefore design is adequate with regards to bearing resistance.

nbR qq φ= (10.6.3.1.1-1)

γγγγ wmwqqmfcmn CBNgCNDgcNq 5.0++= (10.6.3.1.2a-1)

c = 0, φ = 30o, γ2 = 105 pcf, and γ2’ = 50 pcf

Nq = 18.4, N γ = 22.4 [Table 10.6.3.1.2a-1]

Cwq= 1 (Dw = Df) [Table 10.6.3.1.2a-2]

Cw γ = 0.5

sq = 1 + (B/L)tanφf =1 (L>>B) [Table 10.6.3.1.2a-3]

sγ = 1 - 0.4(B/L) =1 [Table 10.6.3.1.2a-3]

dq = 1 [Table 10.6.3.1.2a-4]

For modest embedment of footing, it is usually to omission of the inclination factors.

Nqm = Nqsqdqiq=18.4x1x1x1=18.4

N γm = N γsγiγ=22.4 x1x1=22.4

5.04.22))18.2)(2(14(105.05.014.182105.0 ××−××+×××=nq = 9.55 ksf/ft

qR = Фqn, use Ф= 0.55 (FDOT recommended)

qR = 0.55x12.1=5.25 ksf/ft

qR > σv in all loading cases , therefore, the footing design is adequate.

c. Check sliding

δφττ tan××= VR where: 9.0

,tantan=

=

τφ

φδ

andf

τR = 0.9x29.4x tan 30o = 15.3 kips/ft > Htotal in all load cases

OK (CDR = 15.3/13.5) = 1.13

Table 3 [Table 11.5.6-1 Resistance Factors for Permanent Retaining Walls.]

25

WALL-TYPE AND CONDITION RESISTANCE FACTOR

Nongravity Cantilevered and Anchored Walls Bearing resistance of vertical elements Article 10.5 applies Passive resistance of vertical elements 1.00 Pullout resistance of anchors(1) • Cohesionless (granular) soils

• Cohesive soils • Rock

0.65 (1) 0.70 (1) 0.50 (1)

Pullout resistance of anchors(2) • Where proof test are conducted 1.0(2) Tensile resistance of anchor tendon

• Mild steel (e.g., ASTM A 615 bars) • High strength steel (e.g., ASTM A 722

bars)

0.90(3) 0.80(3)

Flexural capacity of vertical elements 0.90

Mechanically Stabilized Earth Walls Bearing resistance Article 10.5 applies Sliding Article 10.5 applies Tensile resistance of metallic reinforcement and connectors

Strip reinforcements(4) • Static loading • Combined static/earthquake loading

Grid reinforcements(4) (5) • Static loading • Combined static/earthquake loading

0.75 1.00

0.65 0.85

Tensile resistance of geosynthetic reinforcement and connectors

• Static loading • Combined static/earthquake loading

0.90 1.20

Pullout resistance of tensile reinforcement

• Static loading • Combined static/earthquake loading

0.90 1.20

Prefabricated Modular Walls

Bearing Article 10.5 Applies Sliding Article 10.5 Applies Passive resistance Article 10.5 Applies

(1) Apply to presumptive ultimate unit bond stresses for preliminary design only in Article C11.9.4.2. (2) Apply where proof test are conducted to a load of 1.0 or greater times the factored design load on the anchor. (3) Apply to maximum proof test load for the anchor. For mild steel apply resistance factor to Fy. For high-strength steel apply the resistance factor to guaranteed ultimate tensile strength. (4) Apply to gross cross-section less sacrificial area. For sections with holes, reduce gross area in accordance with Article 6.8.3 and apply to net section less sacrificial area. (5) Applies to grid reinforcements connected to a rigid facing element, e.g., a concrete panel or block. For grid reinforcements connected to a flexible facing mat or which are continuous with the facing mat, use the resistance factor for strip reinforcements.

Table 4

26

Resistance Factors for Geotechnical Resistance of Shallow Foundations at the Strength Limit

State. (Table 10.5.5.2.2-1, AASHTO 2006)

Method/Soil/Condition Resistance Factor

Theoretical method (Munfakh et al., 2001) in clay 0.5

Theoretical method (Munfakh et al., 2001) in sand, CPT 0.5

Theoretical method (Munfakh et al., 2001) in sand, SPT 0.45

Semi-emperical methods (Meyerhof,1957), all soils 0.45

Footing on rock 0.45

Bearing

Resistance φb

Plate load test 0.55

Precast concrete placed on sand 0.90

Cast-in-place concrete on sand 0.80

Cast-in-place or Precast concrete on clay 0.85 φτ

Soil on soil 0.90

Sliding

φep Passive earth pressure component of sliding resistance 0.50

3.3 Internal Stability

It is titled as ‘Safety against Structural Failure’ in AASHTO Section 11.10.6. In this

section, it requires engineers to evaluate the pullout resistance and rupture of soil

reinforcements.

3.4.1 Maximum reinforcement loads Simplified Method approach should be used to calculate the maximum reinforcement loads. )( HrVPH k σσγσ Δ+= (11.10.6.2.1-1)

where: γP = load factor for EV

kr = horizontal pressure coefficient

σv = vertical pressure due the reinforced soil mass and any surcharge loads above it.

ΔσH= horizontal stress at reinforcement level resulting from any applicable concentrated horizontal surcharge loads.

27

Figure 13 – Live Load and Dead Load

Surcharges for Internal Stability Analysis

for Horizontal Backfill

Figure 14 – Live Load and Dead Load

Surcharges for Internal Stability Analysis

for Slope Backfill

Figure 15 – Variation of Coefficient of Active

Lateral Earth Pressure Multiplier Factors with

Depth

3.4.2 Maximum tension force

The maximum tension force applied to the reinforcements per unit width of the wall

will be;

VH ST σ=max (11.10.6.2.1-2)

Where: σH = factored horizontal soil stress at the reinforcement

28

Sv = vertical spacing between reinforcements (< 2.7 ft.)

Figure 16 Potential Failure Surface for Internal Stability Design of MSE Walls

3.4.3 Pullout Resistance Length

The potential failure surface for inextensible and extensible wall system and the active

and resistant zones are shown in Figure 16. The pullout resistance length shall be determined

using the following equation;

cv

e CRFTLασφ *

max≥ (11.10.6.32-1)

Where: Le = length of reinforcement in resistant zone (ft.) >= 3’

29

Tamx = factored tension load in reinforcement (kips/ft)

ø = resistance factor for reinforcement pullout

F* = pullout friction factor, need not be reduced for properly placed and

compacted, saturated backfill (per FDOT Structures Design Guidelines

section 3.13).

α = scale effect correction

factor

σv = unfactored vertical stress

at reinforcement level

C = overall reinforcement

surface area geometry factor based on the gross perimeter of the

reinforcement, equal to 2 for strip, grid and sheet, i.e., two sides

Rc = reinforcement

coverage ratio

Figure 17 Default Values for Pullout

Friction Factor, F*

Soil reinforcements, in general,

should be designed laying perpendicular to the back of the wall facing panels. If this not

feasible because of obstructions, such as piles or other miscellaneous structures, the clearance

between the wall panels and obstructions shall be increased such that the soil reinforcement is

skewed no more than 15 degree off the perpendicular as per SDG. The pullout resistance

should be separately with the consideration of the skewed angles.

30

3.3.4 Reinforcement Strength

The reinforcement strength shall be checked at every level within the wall, both at the

boundary between the active and resistance zones (i.e., zone of maximum stress), and at the

connection of the reinforcement to the wall face.

• Zone of maximum stress

cal RTT φ=max

Where: Tmax = factor load to the reinforcement (kips/ft)

Ø = resistance factor for reinforcement tension

Tal = nominal long term reinforcement design strength (kips/ft)

For steel reinforcement; bFA

T ycal = , and

For geosynthetic reinforcement; RFTTal

max= RF=RFID x RFCR x RFD

Rc = reinforcement coverage ratio.

• Stress at the connection with the wall face

caco RTT φ=

Where: To = factor load at the reinforcement/facing connection (kips/ft)

Ø = resistance factor for reinforcement tension in connectors

Tac = nominal long term reinforcement/facing connection design strength (kips/ft)

Rc = reinforcement coverage ratio.

3.3.4 Design Life Consideration for Soil Reinforcement

In SDG section 3.13, Corrosion Rate for non-corrosive environments (low and moderate air

contaminants):

(A) Zinc (first 2 years) 0.59mils/year

(B) Zinc (subsequent years to depletion) 0.16mils/year

(C) Carbon Steel (after depletion of zinc) 0.48mils/year

(D) Carbon Steel (75 to 100 years) 0.28mils/year

Example 3 – MSE Wall Internal Stability

Wall height

31

PEV1

PVT

1.25

e

PaH

γp σv=quniform

PLS

L

H = 20 feet, Df = 2

Reinforced soil mass:

Assume 40mm x 5 mm ribbed steel strips will be used

φr = 30o

γr = 105 pcf

Traffic/live loads:

q = 250 psf/ft

ka = tan2(45 – φ/2) = 0.333

Step 1 – Calculate the factored horizontal force acting on the reinforcement

For this example assume steel strips reinforcements are used, at vertical spacing of Sv

= 2.5’ beginning at 1.25’ below the top of the wall. The vertical pressure at the reinforcement

is the vertical earth pressure uniformly distributed over an adjusted reinforcement length of

L’=L – e.

The load case that produces the largest uniform stress is Strength Ib, i.e. γEV = 1.35

and γEH = 1.5. Live load surcharge is not considered in the internal stability calculations for

vertical pressure. The factored vertical pressure as well as horizontal earth pressure is

calculated at each layer or

reinforcement strip determines the

eccentricity of each layer.

riEVEVi ZP γγ=

= 1.35*Zi*0.105

= 0.1418Zi

Zi= depth from the top of the

wall to the i reinforcement.

At level 1 reinforcement, where L=14’

)(1 ZiLP rEVET ×××= γγ = 1.35*14* 0.105*1.25= 2.48 kips/ft

21LPM ETV ×= =2.48*7 = 17.36 kips-ft/ft

)21()

21

31( 22

LSiariiaEHH qZKlshZZKM ××××+××××××= γγγ

= (1.5*0.333*0.333*1.25*0.5*1.252*0.105) +(1.75*0.333*0.5*1.252*0.25]

= 0.131 K-ft/ft

D

0.3

0 5

32

EV

HV

PMMLe −

−=2

= 7 - 48.2

131.036.17 − = 0.05’

eL

Pq TV

uniformVP 2−==σγ = 0.178

Layer,i Zi (ft) PVT, (kip/ft) MV(kips-ft/ft) Mh (kip-ft/ft) e, ft quniform, (ksf) 1 1.25 2.48 17.36 0.13 0.05 0.178 2 3.75 7.44 52.08 1.49 0.20 0.547 3 6.25 12.4 86.8 4.98 0.4 0.940 4 8.75 17.35 121.55 11.43 0.66 1.369 5 11.25 22.31 156.28 21.66 0.97 1.851 6 13.75 27.26 191.01 36.49 1.34 2.409 7 16.25 32.25 225.74 56.74 1.76 3.077 8 18.75 37.21 260.47 83.22 2.24 3.906

Since the wall is only 20 feet height, the multipliers of lateral coefficient of earth pressure

vary linearly from 1.7 at the top of the wall to 1.2 at 20 feet below the top of the wall.

Therefore, Kr = [1.7 - Zi * (1.7 – 1.2)/20]*Ka = (1.7 - 0.025Zi)*Ka

σH=γp σvKr , and

Tmax = σHsvi

Summary of Factored Horizontal Load at Reinforcements

Layer Zi (ft) γp σv (ksf) Kr σH, (ksf) svi, ft Tmax (kips)

1 1.25 0.178 0.556 0.099 2.5 0.25 2 3.75 0.547 0.535 0.293 2.5 0.73 3 6.25 0.940 0.514 0.483 2.5 1.21 4 8.75 1.369 0.493 0.675 2.5 1.69 5 11.25 1.851 0.472 0.875 2.5 2.19 6 13.75 2.409 0.452 1.088 2.5 2.72 7 16.25 3.077 0.431 1.326 2.5 3.31 8 18.75 3.906 0.410 1.601 2.5 4.00

Step 2 Check pullout resistances

A

TCRF

TLcv

emax

*max =≥

ασφ= length of reinforcement in resistant zone (ft.) >= 3’

Tmax = factored tension load in reinforcement (kips/ft)

ø = 0.9 from Table 2 [AASHTO Table 11.5.6-1]

F* = varies from 1.2 + log Cu (assume Cu = 4) at the top to

tan φr= tan 30 = 0.577 at 20 feet below the top for ribbed steel

strip, i.e. 1.8 to 0.577 or at each reinforcement level F*i = 1.8 –

33

0.06*Zi

α = 1 for steel reinforcements

σv = unfactored vertical stress at reinforcement level

C = 2 (for strip)

Rc = b/Sh = (40/25.4)/ 40 = 0.03937 [ Sh = 40” is predetermined]

Layer Zi (ft) σv (ksf)/ft F* A Tmax /ft(kips) Le, ft 1 1.25 0.131 1.724 0.016 0.25 15.4 2 3.75 0.394 1.575 0.045 0.73 16.2 3 6.25 0. 656 1.425 0.07 1.21 17.3 4 8.75 0.919 1.275 0.091 1.69 18.6 5 11.25 1.181 1.125 0.108 2.19 20.3 6 13.75 1.444 0.975 0.121 2.72 22.4 7 16.25 1.706 0.825 0.13 3.31 25.4 8 18.75 1.969 0.675 0.134 4.00 29.9

A = ø F* α σv C Rc

L = La + Le

Active zone, La

Z =0 - 0.5 H or 0’ - 10’ La= 0.3 H = 6’

Z = 0.5H – H or 10’ – 20’ La varies from 6’ - 0’

Layer Zi (ft) Le, ft La, ft L, ft 1 1.25 15.4 6 21.4 2 3.75 16.2 6 22.2 3 6.25 17.3 6 23.3 4 8.75 18.6 6 24.6 5 11.25 20.3 5.25 25.6 6 13.75 22.4 3.75 26.2 7 16.25 25.4 2.25 27.7 8 18.75 29.9 0.75 30.7

The longest L is at Z8,

L = 29.9 + .75 = 30.7’ say 31’

Thus internal stability controls the design of reinforcement length at all layers. Adjust

the lengths to whole number (rounding up), which resulting in longer Le .

34

Layer Zi (ft) A Actual Le, ft Actual

Resistance*, (kips)/ft

Tmax (kips)/ft

1 1.25 0.016 16.00 0.26 0.25 2 3.75 0.045 17.00 0.77 0.73 3 6.25 0.07 18.00 1.26 1.21 4 8.75 0.091 19.00 1.73 1.69 5 11.25 0.108 20.75 2.24 2.19 6 13.75 0.121 23.25 2.81 2.72 7 16.25 0.13 25.75 3.35 3.31 8 18.75 0.134 30.25 4.05 4.00

* Resistance = (Actual Le, ft) x A, where A= cvCRF ασφ *

Since the actual resistance at each reinforcement level is larger than that of the

maximum tensile stress required for pullout, therefore the design is adequate.

Step 3 – Check Reinforcement Strength

The engineer should also check the tensile stress at the connection and the

design life based on the corrosion rate. Assume they are OK.

4.0 Nongravity Cantilever Walls (AASHTO 3.11.5.6). 4.1 Granular Soils or Rock

For permanent walls the simplified lateral earth pressure distributions as shown in

Figures 17 through 19 may be used. For temporary walls with discrete vertical elements,

Figures 17 & 18 may be used to determine passive resistance and Figures 20 & 21 may be

used to determine the active earth pressure due to the retained soil.

35

Figure 17 Figure 18

Figure 19 Figure 20

36

Figure 21

Figure 23

Figure 22

37

4.2 Cohesive Soils

If walls will support or are supported by cohesive soils for temporary applications,

wall must be designed based on total stress methods of analysis and undrained shear strength

parameters. Figures 20 – 23 may be used with the restrictions of;

• Ratio of total overburden pressure to undrained shear strength, Ns ( ;u

ss S

HN γ= γs =

total unit weight; H = total excavation depth, and Su = average undrained shear

strength of soil. AASHTO 3.11.5.7.2)

• The active earth pressure shall not be less than 0.25 times the effective overburden

pressure at any depth, or 0.035 ksf/ft of wall height, whichever is greater.

A portion of negative loading at top of wall due to cohesion is ignored and hydrostatic

pressure in a tension crack should be considered.

4.3 Nongravity Cantilevered Walls Design

Article 11.8 outlines the design and analysis. In C11.8.4.1 particularly it states the

procedures to determine the value x using factored loads as well as resistance factor. However,

at the end, the design embedment length shall also be extended by 20%, which is the same as

the design method of the old. With the combination of maximum load factor, the reduced

resistance factor and the 20% increase, we found that too much conservatism is built into the

design. Thus, we think the old method should be used because there aren’t many case

histories of failure.

Appendix

Changes in FDOT’s Structures Design Guidelines and Plans Preparation Manual are in the

Appendix.

i. Attachment A - Structural Manual Vol. 1; Structures Design Guidelines – Section 3.13

ii. Attachment C – Plans Preparation Manual – Vol. 1; Section 30.2.3, 30.2.4 and

Flowchart and Table of FDOT Wall Types