Stress Strain in Pavements

Stress and Strain in PavementsByHaiping Zhou, MACTEC E&C Inc.

For CSU, Chico, CIVL 581 Transportation PavementsSeptember 14, 2006

*

OutlineWhat is stress and strain?Stress and strain in flexible pavementsStresses in rigid pavementsDetermination of modulusKENPAVE software

*


*

StressForce per unit area

Units: MPa, psi, ksiTypes: bearing, shearing, axialPAs = LoadArea=

*

StrainRatio of deformation caused by load to the original length of material

Units: Dimensionless

*

StiffnessStiffness = stress/strain = For elastic materials:Modulus of ElasticityElastic ModulusYoungs ModulusStress, Strain, E1

*

Stress vs. Strain of a Material in Compression

*

Poissons Ratio

*

Typical Modulus (E) Values

*

Material Range (ksi) Typical (ksi) PCC 3,000 - 8,000 4,000HMA 200 - 800 450ATB 70 - 450 150Granular soil 7 - 22 15Fine-grained soil 3 - 10 4Granular base 14 - 50 30CTB 500 - 1,000 700Lean concrete 1,000 - 3,000 1,500Typical Modulus Values

*

Typical E Values Asphalt Concrete

*

Material Range Typical PCC 0.10 - 0.20 0.15HMA / ATB 0.15 - 0.45 0.35Cement Stab. 0.15 - 0.30 0.20BaseGranular 0.30 - 0.40 0.35Base / SubbaseSubgrade Soil 0.30 - 0.50 0.40Typical Poissons Ratios

*

Deflection (D)Change in lengthDeformationUnits: mm, mils (0.001 in)

*

Structural Response ModelsDifferent analysis methods for AC and PCC Layered system behavior All layers carry part of load Slab action predominates Slab carries most load

*


*

Flexible Pavement Model

*

Layered Elastic SystemsThe basic assumptions:Each layer is homogeneous, isotropic, and linearly elastic with an elastic modulus and mThe material is weightless Each layer has a finite thickness, except the lowest layerA uniform pressure is applied over a circular areaInterface condition (continuity vs frictionless)

*

Pavement Response Locations Used in Evaluating Load Effects

*

Stresses and Strains in Flexible PavementsFunction of the following:Material properties of each layerThickness of each layerLoading conditionsPavement responses generally of interest:Surface deflectionHorizontal tensile strains at bottom of AC layerVertical compressive strain on top of intermediate layer (base or subbase)Vertical compressive strain on top of the subgrade

*

One-Layer System (Boussinesq)The original elastic theory published by Boussinesq in 1885For computing stresses and deflections in a half-space (soil) composed of homogeneous, isotropic, and linearly elastic materialStill widely used in soil mechanics and foundation design

*

One-Layer System

*

One-Layer System(Cylindrical Coordinates)

*

Formulas for Calculating Stresses

*

Two-Layer System (Burmister)Burmister extended the one-layer solutions to two and three layers in 1943Assumed layers have full frictional contact at the interface and m=0.5Equation and graphs are used to compute deflection

*

Two-Layer System

*

Two-Layer SystemDisplacement coefficient IDz

*

Two-Layer SystemVertical stress influence coefficient z/p, for a=h

*

Multi-Layer System

*

Method of Equivalent Thicknesses (General Equation)hei = calculated equivalent thickness for ith layerhi = layer thickness for ith layerEi = modulus for ith layerEi+1 = modulus for (i+1)th layermi = Poissons ratio for ith layermi+1 = Poissons ratio for (i+1)th layer

*

Formulas for Calculating Stresses

*

Multi-Layer SystemComputer programsKENLAYERELSYM5LEAP2EVERSTRSTypical inputMaterial properties: modulus and mLayer thicknessLoading conditions: magnitude of load, radius, or contact pressure

*

Resilient Modulus vs. Bulk Stress for Unstablized Coarse Grained Materials

*

Resilient Modulus vs. Deviator Stress for Unstablized Fine Grained Materials

*

Pavement Response Locations Used in Evaluating Load Effects

*

Example AC Fatigue Criterion

*

Example Subgrade Strain Criterion for Rutting

*

Example Pavement (6 Base)

*


*


*


*

Stresses in Rigid PavementsWarping stressesLocations: edge; interior; cornerWheel load related stressesLocation: edge; interior; cornerShrinkage/expansion stressesOther stresses

*

Warping Stress - Day Time(Slab surface temp>bottom temp)

*

Warping Stress - Night Time(Slab bottom temp>surface temp)

*

Constrained Transverse Joints(Slab surface temp>bottom temp)

*

Warping Stress - EdgeBy BradburyWhere:t =slab edge warping stress (psi)E =modulus of elasticity of PCC (psi)e =thermal coefficient of PCC (~0.000005/F)DT =temperature differential between the top and bottom of the slab (F)C =coefficient, function of slab length and the radius of relative stiffness, L

*

Radius of Relative Stiffness

*

Warping Stresses Coefficient

*

Warping Stress - InteriorBy BradburyWhere:t =slab interior warping stress (psi)E =modulus of elasticity of PCC (psi)e =thermal coefficient of PCC (~0.000005/F)m =Poissons ratio for PCCC1 =coefficient in direction of calculationC2 =coefficient in direction perpendicular to C1

*

Warping Stress - CornerBy BradburyWhere:t =corner warping stress (psi)E =modulus of elasticity of PCC (psi)e =thermal coefficient of PCC (~0.000005/F)DT =temperature differential between the top and bottom of the slab (F)m =Poissons ratio for PCCa =radius of wheel load distribution for corner loadL =radius of relative stiffness

*

Load Stress - Westergaard

*

Load Stress - WestergaardWhere:W =wheel load (lb)h =slab thickness (in.)a =radius of wheel contact area (in.)L =radius of relative stiffness (in.)b =radius of resisting section (in.)

*

Load Stress - WestergaardWhere:b =equivalent radius of resisting section (in.)a =radius of wheel contact area (in.), and h = slab thickness (in.)

*

Slab Expansion/ContractionWhere:z =joint opening (or change in slab length, in.)C =base/slab frictional restrain factor (0.65 for stabilized bases; 0.80 for granular bases) L = slab length (in.)e = PCC coefficient of thermal expansion by aggregate type (e.g., 6.0x10-6/F for gravel; 3.8x10-6/F for limestone)Dt =the maximum temperature ranged =shrinkage coefficient of concrete (e.g., 0.00045 in./in. for indirect tensile strength of 500 psi)

*

Westergaards Model of Subgrade Reaction

*

Slab Deflection to a Load

*


*

Determination of ModulusLaboratory testsBound materialsUnbound materialsField testsDestructive testsNon-destructive test

*

StiffnessStiffness = stress/strain = For elastic materials:Modulus of ElasticityElastic ModulusYoungs ModulusStress, Strain, E1

*

Resilient Modulus TestAxial CompressionUsed primarily for testing of bound materials (prepared specimens or core samples)OEM, Inc. 2000LoadRamLoad CellLVDTGage Length Heavier duty test equipment is used to measure compressive strength

*

Coring

*

Core Samples

*

Pavement Core

*

Resilient Modulus TestTriaxial CompressionUsed primarily for testing of unbound materials (re-compacted specimens or push tube samples)

*

Hveem Resistance Test(R-value) Stiffness measure for unbound materialsStandard axial stress (v) is appliedR-value is basically the ratio of the applied vertical pressure (v) to the developed lateral pressure (h)vh150mm100 mm

*

California Bearing Ratio (CBR) TestStrength measure for unbound materialsPiston advanced at 1.3 mm / min. rateMeasure load at 2.5 mm penetration (P2.5)CBR = 100(P2.5/Pstd)SaturatedSpecimen50 mmdiameterpiston150 mm180mm

*

Estimation of Elastic Modulus of PCC (ACI 318)Ec = (Wc)1.5 (33)(fc)0.5

Where:Ec = Static elastic modulus, psiWc = Unit weight of PCC, pcf (90-155)fc = Specified compressive strength for 6x12 cylinders (

Documents

Stress Strain in Pavements