National Academies Press: OpenBook
« Previous: Appendix D. Moisture-Sensitive, Stress-Dependent, and Cross- Anisotropic Resilient Modulus
Page 180
Suggested Citation:"Appendix E. Slab-Base Interface Shear Bonding Model." National Academies of Sciences, Engineering, and Medicine. 2019. Proposed Enhancements to Pavement ME Design: Improved Consideration of the Influence of Subgrade and Unbound Layers on Pavement Performance. Washington, DC: The National Academies Press. doi: 10.17226/25583.
×
Page 180
Page 181
Suggested Citation:"Appendix E. Slab-Base Interface Shear Bonding Model." National Academies of Sciences, Engineering, and Medicine. 2019. Proposed Enhancements to Pavement ME Design: Improved Consideration of the Influence of Subgrade and Unbound Layers on Pavement Performance. Washington, DC: The National Academies Press. doi: 10.17226/25583.
×
Page 181
Page 182
Suggested Citation:"Appendix E. Slab-Base Interface Shear Bonding Model." National Academies of Sciences, Engineering, and Medicine. 2019. Proposed Enhancements to Pavement ME Design: Improved Consideration of the Influence of Subgrade and Unbound Layers on Pavement Performance. Washington, DC: The National Academies Press. doi: 10.17226/25583.
×
Page 182
Page 183
Suggested Citation:"Appendix E. Slab-Base Interface Shear Bonding Model." National Academies of Sciences, Engineering, and Medicine. 2019. Proposed Enhancements to Pavement ME Design: Improved Consideration of the Influence of Subgrade and Unbound Layers on Pavement Performance. Washington, DC: The National Academies Press. doi: 10.17226/25583.
×
Page 183
Page 184
Suggested Citation:"Appendix E. Slab-Base Interface Shear Bonding Model." National Academies of Sciences, Engineering, and Medicine. 2019. Proposed Enhancements to Pavement ME Design: Improved Consideration of the Influence of Subgrade and Unbound Layers on Pavement Performance. Washington, DC: The National Academies Press. doi: 10.17226/25583.
×
Page 184

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.

E-1 Appendix E. Slab-Base Interface Shear Bonding Model The interface shear bonding,  , in Eq. E.1 is expressed by the ratio of in-situ shear stress, 2( ) fzx  , in the base course on the slab-base interface, and the shear stress, 2v , in the base layer on the interface when full shear is transferred. 2 2 2 ( ) , ( ) f f zx zx fsv       (E.1) where fs is the shear strength of the base course. Figure E.1. Illustration of In-situ Shear Stress in the Base Course on the PCC-Base Interface Using a Mohr-Coulomb Failure Envelope. Figure E.1 shows a schematic figure of the developed shear stress in the Portland Cement Concrete (PCC)-base interface. The parameters 1v and 2v are shear stress on the interface in the slab and base layer, respectively, when full shear is transferred. The parameter 2( ) fzx  is the shear stress in the base course on the interface for in situ conditions, which is limited by the shear strength, fs , of the base course on the failure plane. When 2( ) fzx  is greater than 2v , the interface is considered as fully bonded. Depending on the ratio of the 2( ) fzx  and 2v , the partial bonding condition is defined in the PCC-base interface. The following section derives the expressions of 2v and 2( ) fzx  . FORMULATION OF V2 The shear stress acting on the two faces of PCC-base interface can be expressed using the theorem of elastic beam shear stress on the transformed section. It is assumed that full shear is transferred through the interface of the transformed section: 1 1 VQv Ib  ; (E.2) 2 2 ( )b s VQv EIb E  (E.3)

E-2 where V is the shear force acting on the cross section. The parameter Q is the first moment of area from the neutral axis of the transformed section; herein 1 1 1Q A d and 2 2 2Q A d . Substituting Eq. E.2 into Eq. E.3 yields: 2 2 1 1 * ( / )b s Qv v Q E E  (E.4) where 1v is determined using the Boussinesq point load solution (97) Figure E.2 illustrates the shear stress acting on the PCC-base interface. Figure E.2. Stresses in Slab-Base Interface Caused by a Point Load. 2 2 2 5/2 2 2 1/ 2 2 2 1/ 2 3 (1 2 ) 2 ( ) ( ) [( ) ] s x s s s s h aP h a h a h a h            (E.5) 3 2 2 5/2 3 2 ( ) s z s hP h a     (E.6) 2 1 2 2 5/2 3 2 ( ) s zx s ahPv h a          (E.7) where P is the surface point load. hs is the thickness of the slab.

E-3 a is the horizontal distance of target point from P.  is the Poisson’s ratio. From Eqs. E.4 and E.7, it is obtained that: 2 2 2 2 5/2 ( )3 2 2 ( ) ( ) 2 b b s s ss s hh h zahPv hh a h z         (E.8) FORMULATION OF (ΤZX)2ΘF The expression of in-situ shear stress in the base course on PCC-base interface is derived using the Mohr-Coulomb failure envelope, as shown in Figure E.3. The failure envelope is defined by the shear strength parameters (i.e., cohesion, c, and friction angle,  ). Figure E.3. Maximum Shear Strength of Base Course in Mohr Coulomb Failure Envelope. 2( ) sin2fzx r  (E.9) where r is the radius of the Mohr’s circle. Herein, the state of plane stress on the slab-base interface is defined by x , z , and zx , which is rotated by an angle of 2 from principal plane of stress. The angle of rotation, 2 , is expressed in Eq. E.10.

E-4   2 2 2 2 3 2 2 2 2 1/22 2 3 ( ) tan2 3( )1 (1 2 )[ ]2 2 ( ) s szx z x s s s s s ah h a h h a h a h a h                       2 2 2 2 1 3 2 2 2 2 1/22 2 3 ( ) 2 tan ( ) 3( )1 (1 2 )[ ] 2 ( ) s s s s s s s ah h a h h a h a h a h                   (E.10) As illustrated by Figure E.3, the shear strength of the base course is calculated by Eqs. E.11 and E.12: c o sfs r  (E.11) ta n [ s i n ] t a nf fs c c r         (E.12) where f is the normal stress on the failure plane. Therefore: ( tan )cosr c     (E.13) Herein, 3 2 2 2 5/2 2 2 1/2 2 2 1/2 3( ) (1 2 )[ ] 2 4 ( ) ( ) [( ) ] z x s s s s s s h h aP h a h a h a h               (E.14) According to Eqs. E.9, E.10, and E.13, it is obtained that:   2 2 2 2 1 2 3 2 2 2 2 1/22 2 3 ( ) ( ) ( tan )cos sin[tan ( )] 3( )1 (1 2 )[ ] 2 ( ) f s s zx s s s s s ah h a c h h a h a h a h                      (E.15) The expression of interface shear bonding,  , is derived from Eqs. E.1, E.8, and E.15:

E-5   2 2 2 2 1 3 2 2 2 2 1/22 2 2 2 2 5/2 3 ( ) ( tan )cos sin[tan ( )] 3( )1 (1 2 )[ ] 2 ( ) ( )3 2 2 ( ) ( ) 2 s s s s s s s b b s s ss s ah h a c h h a h a h a h hh h zahP hh a h z                            (E.16) The ranges of the parameters in ANN model are given in Table E.1. Table E.1. Selected Range of Input Parameters in ANN Training Dataset Input parameters Level Input values PCC thickness (mm) 3 178, 254 and 348 Base thickness (mm) 3 101.6, 203.2 and 254 PCC modulus (MPa) 3 14420, 41400, and 82737 Base modulus (MPa) 4 69, 690, 6894 and 25000 Subgrade modulus (MPa) 3 34.5, 282 and 551 PCC-base interface bonding 4 0, 0.3, 0.6, and 1

Next: Appendix F. Sensitivity Analysis of Modulus of Subgrade Reaction Model »
Proposed Enhancements to Pavement ME Design: Improved Consideration of the Influence of Subgrade and Unbound Layers on Pavement Performance Get This Book
×
MyNAP members save 10% online.
Login or Register to save!
Download Free PDF

The performance of flexible and rigid pavements is known to be closely related to properties of the base, subbase, and/or subgrade. However, some recent research studies indicate that the performance predicted by this methodology shows a low sensitivity to the properties of underlying layers and does not always reflect the extent of the anticipated effect, so the procedures contained in the American Association of State Highway and Transportation Officials’ (AASHTO’s) design guidance need to be evaluated.

NCHRP Web-Only Document 264: Proposed Enhancements to Pavement ME Design: Improved Consideration of the Influence of Subgrade and Unbound Layers on Pavement Performance proposes and develops enhancements to AASHTO's Pavement ME Design procedures for both flexible and rigid pavements, which will better reflect the influence of subgrade and unbound layers (properties and thicknesses) on the pavement performance.

  1. ×

    Welcome to OpenBook!

    You're looking at OpenBook, NAP.edu's online reading room since 1999. Based on feedback from you, our users, we've made some improvements that make it easier than ever to read thousands of publications on our website.

    Do you want to take a quick tour of the OpenBook's features?

    No Thanks Take a Tour »
  2. ×

    Show this book's table of contents, where you can jump to any chapter by name.

    « Back Next »
  3. ×

    ...or use these buttons to go back to the previous chapter or skip to the next one.

    « Back Next »
  4. ×

    Jump up to the previous page or down to the next one. Also, you can type in a page number and press Enter to go directly to that page in the book.

    « Back Next »
  5. ×

    To search the entire text of this book, type in your search term here and press Enter.

    « Back Next »
  6. ×

    Share a link to this book page on your preferred social network or via email.

    « Back Next »
  7. ×

    View our suggested citation for this chapter.

    « Back Next »
  8. ×

    Ready to take your reading offline? Click here to buy this book in print or download it as a free PDF, if available.

    « Back Next »
Stay Connected!