Structural Design of Rigid Pavementsg g

bbyDr. Peijun Guo

Department of Civil EngineeringDepartment of Civil Engineering

Text Sections: M&F 11.2, 13, 15e t Sect o s & , 3, 5Huang Chapter 12

FLOWCHART FOR PAVEMENT DESIGN

WATER! FROST!

Integrated ClimaticM d l

Material Properties

??

WATER! FROST!

Model

Traffic Loadings AnalysisPavementTraffic Loadings Analysis Structure

Pavement Response

Distress Prediction

Pavement Response

Distress Prediction

Rigid Pavementg

Longitudinal joint

Surface smoothnessor rideability

Thickness Design

Transverse joint

Surface Texture

Concrete materials

Subgrade

Dowel barsTiebars

gSubbase or base

AASHTO Design Methodg

Design ConsiderationDesign Consideration

• Pavement performance• Traffic• Traffic• Roadbed soil/Slab characteristics• EnvironmentEnvironment• Reliability• life cycle cost (LCC)• Shoulder design

AASHTO Design Methodg

• Applicable to JPCP, RCP and CRCP• Similar to AASHTO design for flexible• Similar to AASHTO design for flexible

pavements• Pavement strength measured by slabPavement strength measured by slab

thickness D (not accurate)

AASHTO

Sl bSlab thickness

WATER! FROST!

√Integrated ClimaticM d l

Material Properties

??

WATER! FROST!

√Model

Traffic Loadings AnalysisPavement√Traffic Loadings Analysis Structure

Pavement Response

√

Distress Prediction

Pavement Response

Distress Prediction

Material Characteristics

Soil (subgrade): CoefficientSoil (subgrade): Coefficient of subgrade reaction k

• k depends on moisture content and density of soil

• k can be estimated if CBR or Mr is known • Design k values are composite k (subbase +

b d )subgrade) • Effective k used to take account of seasonal

variation (similar to that for flexible pavement)variation (similar to that for flexible pavement)

Soil Types and k-valueyp

Type of Soil  Support k Values MPa/m CBRyp pp(psi/in3 )

Fine‐grained soils in which silt and l i i l d i

Low  20 to 34 

(75 to 120 )2.5 to 3.5 

clay‐size particles predominate  (75 to 120 )

Sands and sand gravel mixtures Medium 35 to 49 4 5 to 7 5Sands and sand‐gravel mixtures  with moderate amounts of sand and clay  

Medium   35 to 49  (130 to 170)  

4.5 to 7.5 

Sands and sand‐gravel mixtures  relatively free of plastic fines  

High   50 to 60 (180 to 220 )

8.5 to 12  

Material Characteristics: Subgrade k Values

Material Characteristics: Concrete Slab

Elastic Modulus EcElastic Modulus Ec (ACI 318, normal weight concrete)

:cf Compressivestrength′( ) 4.73 ( )c cE GPa f MPa′=

strength( ) 57,000 ( )c cE psi f psi′=

1.5( ) 0.043 ( )c cE GPa f MPaρ ′=

ρ: unit weight of concrete, kN/m3

Material Characteristics: Concrete Slab

Flexural strength (Modulus of rapture)Flexural strength (Modulus of rapture)

Third-point Loading

( ) 0.556 ( )C cS MPa f MPa′ ′=

Third point Loading

( )( )CS or MR psi′ =

′

L/3

d=L/3( )8 ~ 10 ( )cf psi′

L/3Span Length = L

WATER! FROST!

√Integrated ClimaticM d l

Material Properties

??

WATER! FROST!

√√Model

Traffic Loadings AnalysisPavement√Traffic Loadings Analysis Structure

Pavement Response

√

Distress Prediction

Pavement Response

Distress Prediction

Traffic analysisy

Similar to Flexible pavement design

AVE. DAILY TRUCK TRAFFIC

0( ) ( ) (365) ( ) ( )fESAL ADT T T GF DL=

DAILY EQ. SINGLE AXLE LOADSANNAUL EQ. SINGLE AXLE LOADS

TOTAL ESALs FOR THE DESIGN PERIOD

TRUCK FACTOR

TOTAL ESALs IN THE DESIGN LANE FOR THE DESIGN PERIOD

( )( )m

T p F A= ∑TRUCK FACTOR

T = THE PERCENTAGE OF TRUCKS IN THE ADTTf = MEAN ESAL PER TRUCK

1( )( )f i i

iT p F A

=

= ∑

Tf MEAN ESAL PER TRUCKGF = TOTAL GROWTH FACTORDL = PERCENTAGE OF TOTAL TRUCK TRAFFIC IN DESIGN LANE

Traffic analysisy

Similar to Flexible pavement design

Rigid EASLs ≠ Flexible EASLs

Since pavement responses are different, the equivalency factors (LEFs) are different

• AASHTO EALF

Rigid pavementRigid pavement

18tN

txN

D: Slab thickness in inch

AASHTO EALF

Ntx = the number of x-axle load applications at the end of tx pptime t;

Nt18 = the number of 80-kN single-axle load applications to time t;time t;

Lx = the load in kip on one single axle, one set of tandem axles, or one set of tridem axle; h l d ( f l l f d lL2 = the axle code (1 for single axle, 2 for tandem axles,

and 3 for tridem axles);

D = Slab thickness (in) 1 in = 25 4 mm;D = Slab thickness (in), 1 in = 25.4 mm; Pt = the terminal serviceability, which indicates the

pavement conditions to be considered as failures; G f i f P d i h l f ( h L iGt = a function of Pt; and β18 is the value of (βx when Lx is

equal to 18 and L2 is equal to one.

WATER! FROST!

√Integrated ClimaticM d l

Material Properties

??

WATER! FROST!

√√Model

Traffic Loading AnalysisPavement√√ Rigid Traffic Loading Analysis Structure

Pavement Response

√√ gpavement

Distress Prediction

Pavement Response

Distress Prediction

Design Criteriag

Primarily considerationsPrimarily considerations

• Fatigue of concrete slab: Pavement structureCracking/Functional failure

• Erosion of subgrade soils: subbase/subgradesubbase/subgrade pumping, joint faulting, etc

• Tensile cracking at the bottom of concrete slab

• Mud pumping

bottom of concrete slab

Erosion Model

Conditions for Pumping• Subgrade Soil that will go into

Suspension• Erodibility of subbase/

Soil• Erodibility of subbase/

subgrade soil• Free water between Slab and

S b dWater

Subgrade• Frequent Heavy wheels loads

/ Large DeflectionsLoad

Currently, no mechanistic models are available

g

y

Erosion Model

F t t b id d- Factors to be considered:

• Subbase and subgrade characteristics• Subbase and subgrade characteristics

• Drainage conditiong

• Joint load transfer effectivenessH i l d t f d t b d il- How is load transferred to subgrade soil

Erosion Model: Pumping Index (PI) p g ( )

Jointed plain concrete pavement

( )0.44318 [ 1.479 0.255(1 ) 0.0604PI N S P= − + − +

1.747 1.20552.65 0.0002269( ) ]H FI−+ +

• Pumping index (PI) on a scale of 0 to 3g0 – no pumping; 1 – low-severity pumping2 – low-severity pumping; 3 – high-severity pumping

• N18 = ESALs; • H = slab thickness (in)• S = soil type: 0 for coarse-grained soils (A-1 to A-3), 1 for fine-grained soils (A-4 to A-7)g ( )• P = annual precipitation (cm)• FI = freezing index (degree days)

Erosion Model: Pumping Index (PI) p g ( )

Jointed reinforced concrete pavement

( )0.670 5.018

0 0395 0 00805

[ 22.82 26,102.2 0.129 0.118PI N H D S−= − + − −0.0395 0.0080513.224 6.834(1 ) ]P FI+ + +

• Pumping index (PI) on a scale of 0 to 3g0 – no pumping; 1 – low-severity pumping2 – low-severity pumping; 3 – high-severity pumping

D= indicator for the presence of drainage systems: 0 for no subdrainage system, 1 for subdrainage systemy

Erosion Model: Pumping Index (PI) p g ( )

JPCP erosion modelJPCP erosion modelN = 289, R2 = 0.68SEE (std error of estimate) = 0 42SEE (std error of estimate) = 0.42

JRCP i d lJRCP erosion modelN = 481, R2 = 0.57SEE = 0.52

Erosion Model: Drainage Characteristicsg

Use Drainage coefficient Cdg

It accounts for

h d i h i i f h b d• the drainage characteristics of the subgrade

• the amount of water the subgrade retains

- sandy material = 1.0

- Similar in concept to flexible pavement terms

Drainage coefficient Cdg

Recommended Values of Drainage Coefficients Cd for Rigid PavementsPercentage of time pavement structure is exposed to

Water removed Less than Greater thanRating within 1% 1-5% 5-25% 25%

Quality of drainage moisture levels approaching saturation

Excellent 2 hours 1.25-1.20 1.20-1.15 1.15-1.10 1.1Good 1 day 1.20-1.15 1.15-1.10 1.10-1.00 1Fair 1 week 1.15-1.10 1.10-1.00 1.00-0.90 0.9Poor 1 month 1 10-1 00 0 81 00-0 90 0 90-0 80Poor 1 month 1.10-1.00 0.8Very poor Never drain 1.00-0.90 0.90-0.80 0.80-0.70 0.7

1.00-0.90 0.90-0.80

(AASHTO 1993)

Erosion model: Load Transfer at Joints

PC slab

Sub-baseWithout subbase: 0% load transfer efficiency

Aggregate interlock:load is transferred via

D l d j i t ith t

shear between aggregate particles below the joint

Doweled joint without subbase: 100% load transfer efficiency

Load Transfer Coefficient J

• A factor used to account for the ability of the pavement to transfer across discontinuities, such as slab joint, or crackscracks

• Used for pavement with dowel bars at the joints, tied shoulders

• Generally increases with increased traffic for a given set of conditions

• If dowels are used the size and spacing must be p gdetermined by local agency procedure ( generally, dowel diameter = 1/8 slab thickness, spacing = 12’ (305 mm)

and length = 18’ (457 mm)and length = 18 (457 mm)

Load Transfer Coefficient J

Y N Y N

Recommended Load Transfer Coefficient J for Various Pavement Types and Design Conditions

Type of shoulder Asphalt Tied PCCYes No Yes No3.2 3.8-4.4 2.5-3.1 3.6-4.2

2.9-3.2 N/A 2.3-2.9 N/A

Load transfer devicesJPCP and JRCPCRCP

(AASHTO 1993)

J i ff t d b th t f h ld- J is affected by the type of shoulder- Shoulder reduces the load transferred to subgrade- Higher load transfer efficiency yields smaller J

AASHTO DESIGN: Reliability Ry

The statistical factors that influence pavementThe statistical factors that influence pavement performance are:

Overall standard deviation ( S0 )is the same as in flexible pavementsZR (standard normal deviate) describes the probability that the serviceability will be maintained over the design life of themaintained over the design life of the pavement.R (reliability) - typical for interstate majorR (reliability) typical for interstate major highway 90% and 50 % for local roads

AASHTO Method: Design Procedureg

1. Determine soil Mr (resilient modulus) for each season, month, week, etc.

2 Determine subbase resilient modulus M for2. Determine subbase resilient modulus Mr for each season, month, week, etc.

3. Determine composite k-value for each3. Determine composite k value for each season

4. Adjust each for rigid foundation5. Determine relative damage of each season6. Determine weighted k-value7 Correct for lost of s pport7. Correct for lost of support

Effective Subgrade Coefficient kg

Depends on:• Roadbed (subgrade) resilient modulus Mr• Roadbed (subgrade) resilient modulus, Mr• Subbase resilient modulus, Mr-SB

Both vary by season

Two Cases for k

Subgrade, Es Subgrade, Es

Granular base, Esb DSB

Subgrade, Es Subgrade, Es

, ( )π µ= −rigidqawE

20 1

2 k = f (MrS bg ade ,sE2

( )π µ= = sq Ek

w a22

1

k f (MrSubgrade , MrSubbase , DSubbase )

, ( )π µ−rigidw a0 1

Effective Subgrade Coefficient kg

Without subbase (semi-infinite subgrade soil)Without subbase (semi infinite subgrade soil)

k (MPa/m) = 2.03Mr(MPa) k ( i) M ( i)/19 4or k (pci) = Mr(psi)/19.4

1 pci 271 3 kN/m3; 1 psi 6 9 kPa1 pci = 271.3 kN/m3; 1 psi = 6.9 kPa

E2( );( )

π µπ µ

= − ⇒ = =−

qa q Ew kE w a

20 2

0

212 1

( )Mr psi( )( ).

=Mr psik pci

18 8µ = 0.4 – 0.5; a = 15 in (381 mm)

Effective Composite k (contd)p ( )

With subbaseWith subbase

Composite Modulus of Subgrade Reaction:p g

k = f (MrSubgrade , MrSubbase , DSubbase )

Use Figure on next slide.

Granular base, Esb DSB

Subgrade, Es

Composite Modulus of Subgrade Reaction

Units:

Mr and E: psi 4Mr and E: psik: pci

13

1 pci =1 psi/in = 271.3kN/m3;

4

1

1 psi = 6.9 kPa

22

Example: How to determine kcompp comp

Given a subbase thickness DSB = 6 in (152Given a subbase thickness DSB 6 in (152 mm) with MrSB = 20000 psi (138 MPa), subgrade soil Mrsg = 7000 psi (48 MPa), sgdetermine kcomp

Composite Modulus of Subgrade Reaction

subbase thickness DSB = 6 in (152 mm) MrSB = 20000 psi (138 MPa)subgrade soil Mrsg = 7000 psi (48 MPa)determine kcomp

Kcomp = 400 pci (108 MN/m3)(108 MN/m3)

Effective Modulus of Subgrade Reactiong

Adjustment of k for Seasonal Variations:• Adjustment of k for Seasonal Variations:

The effective modulus of subgrade reaction is an gequivalent k that would result in the same damage is seasonal values were used through the year

( )3.420.75 0.7250.3ru D k= −Damage-k relation:

k ( i) h ld b k i li blk (pci) should be kcomp is applicable; D = concrete slab thickness (in)

( )3.420 75 0 725( )3.420.75 0.7250.3ru D k= −

Chart for estimating relative damage to rigid pavements. Source: AASHTO, 1993

Effective Modulus of Subgrade Reactiong

( )3 42Adjustment of the coefficient of subgrade reaction f S l V i ti ( )3.420.75 0.250.39ru D k= −for Seasonal Variations:

From the chart l t lidon last slide

Effective Resilient modulus (MR)( R)

Adjustment of Roadbed (Subgrade) Mr for(Subgrade) Mr for Seasonal Variations

8 2.321.18 10f ru M −= × ×

Loss of Support (LS)pp ( )

Accounts for the potential loss of support arising from subbase erosion (or mud pumping) and/or differential vertical soil movements.Incorporated in design by reducing the kof the materials beneath the slab

Loss of Support (LS)

Loss of Support (LS)Type of material

pp ( )

pp ( )

0.0 to 1.0

0.0 to 1.0

yp

Cement-treated granular base (E = 1 ∗ 106 to 2 * 106 psi)

Cement aggregate mixtures (E = 500,000 to 1 * 106 psi)

0.0 to 1.0

0.0 to 1.0

Asphalt-treated bases (E = 350,000 to 1 *106 psi)

Bituminous-stabilized mixture (E = 40,000 to 300,000 psi)

1.0 to 3.0

1.0 to 3.0

Fi i d t l b d t i l (E 3000 t

Lime-stabilized materials (E =20,000 to 70,000 psi)

Unbound granular materials (E = 15,000 to 45,000 psi)

2.0 to 3.0Fine-grained or natural subgrade materials (E = 3000 to 40,000 psi)

Note: High LS induces more reduction of k valueg

1 psi = 6.9 kPa, 1000 psi = 6.9 MPa

Loss of Support (LS)pp ( )

Correction of effective modulus of subgrade reaction due to loss of foundation contact (1 pci = 271.3 kN/m3)

AASHTO Method: Determination of k

1. Determine soil Mr (resilient modulus) for each season, month, week, etc.

2 Determine subbase resilient modulus M for2. Determine subbase resilient modulus Mr for each season, month, week, etc.

3. Determine composite k-value for each3. Determine composite k value for each season

4. Adjust each for rigid foundation5. Determine relative damage of each season6. Determine weighted k-value7 Correct for lost of s pport7. Correct for lost of support

AASHTO Method

h l d ( d )Mechanistic-empirical designs (M-E designs)

combined both mechanistic and empirical paspectsmechanistic component involves determining pavement responses to loading (σ ε ∆)pavement responses to loading (σ, ε, ∆) using mathematical modelsempirical component relates the pavement

t fresponses to performanceeach key distress type is associated with a critical pavement responsecritical pavement response

AASHTO Method

M-E DESIGNS: FRAMEWORK AND COMPONENTS

INPUTSSTRUCTURAL RESPONSE MODELSSTRUCTURAL RESPONSE MODELSPERFORMANCE PREDICTIONFAILURE CRITERIAFAILURE CRITERIADESIGN RELIABILITY

Summary: Design Inputsy g p

W18 = design traffic (18-kip or 80 kN ESALs)W18 design traffic (18 kip or 80 kN ESALs)ZR = standard normal deviateS0 = combined standard error of traffic andS0 combined standard error of traffic and performance prediction∆PSI = difference between initial and terminal serviceability indicespt = terminal serviceability index (implicit in tflexible design)

All consistent with flexible pavements!

Summary: Additional Design Inputsy g p

S ′= modulus of rupture for concreteSc modulus of rupture for concreteJ = joint load transfer coefficientC drainage coefficientCd = drainage coefficient (similar in concept to flexible pavement terms)

Ec = modulus of elasticity for concretek = modulus of subgrade reaction

Additional inputs reflect differences in materials and structural behaviorin materials and structural behavior.

Design Chartsg

From the AASHTO Guide for Design of Pavement Structures

Design ChartsCharts

From the AASHTO Guide for Design of Pavement Structures

AASHTO Method: Design Procedureg

1. Determine material properties, including the effective p p , gresilient modulus and the composite k-value

2. Select the design serviceability loss 3 Select a level of reliability R and the overall standard3. Select a level of reliability R and the overall standard

deviation S0 (0.3-0.5)4. Assume an D (slab thickness) and estimate the total

b f k l l l l d ( )number of 80 kN equivalent single-axle loads (ESALs) for the design period

5. Determine the concrete slab thickness D

• Is the calculated D close to the assumed D assumed? • If No, assume a new D closer to the calculated in this ,

step and repeat step 4, otherwise ok

Design Exampleg p

Given k (effective) = 72 pci (19.5 MN/m3),Given k (effective) 72 pci (19.5 MN/m ), Ec = 5x106 psi (34.5MPa), Sc = 650 psi (4.5 MPa), J = 3.2, Cd = 1.0, ∆PSI = 4.2-2.5 = 1.7, R = 95%, S0 = 0.25, and ESALs = 5.1x 106, determine thickness D

Design Chartsg

2 52

3

5

14

From the AASHTO Guide for Design of Pavement Structures

Design ChartsCharts

69

10

8

7

From the AASHTO Guide for Design of Pavement Structures

Type Design in Canadayp g

Source: PCC pavements: Some Findings from US-LTPP and Canadian Case Studies, C-SHRP technical brief #22

Highway 407, ON 280 mm JPCP 100 mm asphalt treated OGDL + 200 mm granular base

Highway 104 Nova 250mm doweled 100mm to 300 mm granular baseHighway 104, Nova Scotia

250mm doweled JPCP

100mm to 300 mm granular base

Canadian Examplesp

Highway 407, ON

280 mm JPCP

100 mm asphalttreated OGDL + 200 mm granular base

Highway 104, Nova Scotia

250mm doweled JPCP

100mm to 300 mm granular base

Autoroute13, Quebec

270 mm

Joint Designg

Joint Typesyp• Contraction• Expansion

C t ti• Construction• Longitudinal

Joint Geometry• Spacing• Layout (e.g., regular, skewed, randomized)• Dimensions

Joint Sealant Dimensions

Types of Jointsyp

Contraction• Transverse• For relief of tensile stresses

ExpansionExpansion• Transverse• For relief of compressive stresses

U d i il b t t d t t• Used primarily between pavement and structures (e.g., bridge)

ConstructionLongitudinal• For relief of curling and warping stresses

Typical Contraction Joint Detailsyp

Typical Expansion Joint Detailyp p

For the relief of compressive stresspDifficult to maintain and no longer in use except at the connection between pavement and structure

(19 mm)

(Huang, 2005)

Typical Construction Joint Detailyp

Usually be placed at the location of theUsually be placed at the location of the contraction joint

(Huang, 2005)

Typical Longitudinal Joint Detailyp g

Full Width Construction

(Huang, 2005)

Typical Longitudinal Joint Detailyp g

Lane at a Time Construction: use key joints toLane-at-a-Time Construction: use key joints to ensure load transfer

(Huang, 2005)

Joint Spacingp g

• Local experience is best guide

• Rules of thumb for plane concrete pavement :

JPCP joint spacing (feet) < 2D (inches)W/L < 1.25W/L < 1.25

8-in (203mm) slab: spacing 16 feet (4.9 m)Canadian experience: Doweled JPCP generally has joints spacing 4.5 to 5 m

Joint Dimensions

Width controlled by joint sealant extensionWidth controlled by joint sealant extensionDepths:• Contraction joints: D/4Contraction joints: D/4• Longitudinal joints: D/3Joints may be formed by:Joints may be formed by:• Sawing• Inserts• Forming

Joint Dimensions

Governed by expected jointexpected joint movement, sealant resilience

(AASHTO, 1993)

Design Inputsg p

z αc

When does aggregate interlocking becomeWhen does aggregate interlocking become ineffective?

When cracks are wider than about 0.9 mm

Sub-base