Quantifying the Influence of Geosynthetics on Pavement Performance (2017)

Below is the uncorrected machine-read text of this chapter, intended to provide our own search engines and external engines with highly rich, chapter-representative searchable text of each book. Because it is UNCORRECTED material, please consider the following text as a useful but insufficient proxy for the authoritative book pages.

B-1 APPENDIX B. DETERMINATION OF GEOSYNTHETIC-AGGREGATE INTERFACIAL PROPERTIES USING PULLOUT TEST The interaction between aggregates and the geosynthetic layer is commonly quantified using the pullout test (1). Figure B-1 is a schematic plot of the pullout test. The geosynthetic embedded in the base course is pulled out of the aggregate layer by a tensile pullout force. The pullout force is recorded and the displacement of the geosynthetic is measured using linear variable differential transformers (LVDTs). The typical pullout test data are shown in Figure B-2, in which the pullout force versus geosynthetic displacement curve has three stages— linear stage, nonlinear stage, and critical stage—each with different mechanisms of aggregate- geosynthetic interaction. The pullout test data in the three stages were interpreted in this project to determine the interfacial shear modulus between the geosynthetic and the aggregates, which are detailed as follows. The purpose of developing the following equations was to determine from readily available test data the effective properties of geosynthetics as they interact with base course material. This provides valuable supplemental information that is useful input to the modifications to the Pavement ME Design software. Figure B-1. Schematic Plot of the Pullout Test

B-2 Figure B-2. Pullout Force versus Geosynthetic Displacement in a Pullout Test Stage 1: Linear without Slipping In Stage 1, the geosynthetic experiences a small amount of displacement under the pullout force. In this stage, the pullout force has a linear relationship with the geosynthetic displacement and no slipping occurs at the interface. Taking the geogrid as an example for the calculation of the interfacial shear modulus, a differential equation is first established based on the force equilibrium principle: 2 2 ( ) 2 ( ) 0 s Ea u x G u x s x δ ∂ − = ∂ (B-1) where E is the elastic modulus of the geogrid; a is the width of the rib; s is the rib spacing; G is the interfacial shear modulus in the linear stage; sδ is the thickness of the shear zone; and ( )u x is the geogrid displacement at different locations. The boundary conditions for solving Equation B-1 are listed in Equations B-2 through B-4: 0 : ( 0) 0x u x= = = (B-2) : ( ) lx l u x l u= = = (B-3) ( ): l Ea u xx l P P s x ∂ = = = ∂ (B-4) With these boundary conditions, a possible solution to Equation B-1 is: ( ) cosh( ) sinh( )u x A x B xβ β= + (B-5) where A , B , and β are unknown coefficients to be determined. Substituting Equation B-5 into Equation B-1 yields: 0 10 20 30 40 50 60 70 80 90 100 0 10 20 30 40 50 60 Pu llo ut Fo rce (k N) Displacement (mm) Nonlinear Stage Critical Stage Linear Stage

B-3 [ ]2 2( ) cosh( ) sinh( ) 0 s Ea G A x B x s β β βδ− + = (B-6) Since [ ]cosh( ) sinh( ) 0A x B xβ β+ ≠ , Equation B-6 can be rewritten as: 2 2 s Gs Ea β δ= (B-7) Using the boundary conditions, Equations B-2 and B-3, A and B are solved as: 0A = (B-8) sinh( ) luB lβ= (B-9) Therefore, the geogrid displacement function ( )u x can be expressed as: 2sinh ( ) 2sinh s l s Gs x Ea u x u Gs l Ea δ δ     =     (B-10) Substituting Equation B-10 into Equation B-4 yields: cosh( ) sinh( ) l l uEaP l s l β β β= (B-11) By solving Equation B-11 for β and then solving Equation B-7, the thickness of the interface shear zone sδ is determined: 2 2 s Gs Ea δ β= (B-12) Since the pullout force has a linear relationship with the corresponding geosynthetic displacement, G can be assigned as the shear modulus of the base aggregate, which is obtained in the triaxial test. Stage 2: Nonlinear without Slipping In Stage 2, the pullout force shows a nonlinear relationship with the geosynthetic displacement and no slipping occurs on the aggregate/geosynthetic interface. The differential formulation for the geogrid is constructed in Equation B-13: 2 2 ( ) 2 ( ) ( ) 0 s Ea u x G x u x s x δ ∂ − = ∂ (B-13) where ( )G x is the interfacial shear modulus as a function of location, which can be formulated as:

B-4 max 1( ) 1 ( ) s G x u x G τ δ = + (B-14) where maxτ is the maximum shear stress to be determined in Stage 3. Substituting Equation B-14 into Equation B-13 yields: 2 2 max ( ) 2 ( ) 0( ) s u x Gsu x EaGu xx Eaδ τ ∂ − = ∂ + (B-15) The boundary conditions are listed in Equations B-16 through B-18: 0 : ( 0) 0x u x= = = (B-16) : ( ) lx l u x l u= = = (B-17) ( ): l Ea u xx l P P s x ∂ = = = ∂ (B-18) A solution of ( )u x is proposed in Equation B-19: ( ) cosh( ) sinh( )u x A x B x Cβ β= + + (B-19) Then Equation B-15 becomes: [ ] [ ] [ ] 2 max 2 cosh( ) sinh( )cosh( ) sinh( ) 0 cosh( ) sinh( )s Gs A x B x C A x B x EaGEa A x B x C β ββ β β δ β β τ + + + − = + + + (B-20) Using the boundary conditions in Equations B-16 to B-18, the three unknown parameters A , B , and C are obtained: 2 2 cosh( ) sinh( ) cosh ( ) sinh ( ) cosh( ) l l Psu l l EaA l l l β β β β β β β − =  − −  (B-21) [ ] 2 2 cosh( ) 1 sinh( ) cosh ( ) sinh ( ) cosh( ) l l Ps l u l EaB l l l β β β β β β β − − =  − −  (B-22) 2 2 sinh( ) cosh( ) cosh ( ) sinh ( ) cosh( ) l l Ps l u l EaC l l l β β β β β β β − =  − −  (B-23) Substituting Equation B-19 into Equation B-14 yields: [ ] max ( ) 11 cosh( ) sinh( ) s GG x A x B x Cβ β τ δ = + + + (B-24)

B-5 where G is the shear modulus of the base aggregates, and sβ , δ , A , B , and C are determined by Equations B-11, B-12, B-21, B-22, and B-23, respectively. Stage 3: Critical State In Stage 3, the friction stress on the aggregate/geosynthetic interface reaches the maximum shear stress, and the interface is at a critical state of slipping. Based on the force equilibrium, maxτ can be calculated as follows: max max 2 P ls τ = (B-25) Therefore, the aggregate-geogrid interfacial shear modulus at different locations can be determined using Equation B-24 based on the pullout test data. The aggregate-geotextile interfacial shear modulus can also be determined using the same method. When the interface slippage is in the linear stage, a simplified equation for the interfacial shear stiffness in the linear stage is expressed as: 2s r Pk l u Δ = ⋅Δ (B-26) where sk is the interfacial shear stiffness, PΔ is the incremental applied pullout force, l is the embedded length of geosynthetic, and ruΔ is the incremental relative displacement. The Large- Scale Tank test measurements presented in this report indicate that the maximum relative displacement between the geosynthetic and aggregate is less than 0.04 inch. This suggests that the interface slippage normally occurring in the geosynthetic-reinforced aggregates is in the linear stage. References 1. Perkins, S.W., and Cuelho, E. V. (1999). Soil-Geosynthetic Interface Strength and Stiffness Relationships from Pullout Tests. Geosynthetic International, Vol. 6, No. 5, pp. 321–346.