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EverFE Theory Manual Bill Davids, Ph.D., P.E.University of MaineDept. of Civil and Environmental EngineeringFebruary 2003EverFE version 2.23 1 1. Introduction EverFE (current version 2.23) is a 3D finite-element analysis tool for simulating the response of jointed plain concrete pavement systems to axle loads and environmental effects. EverFE couples a highlyinteractive graphical user interface for model development and result visualization written inTcl/Tk/Tix/vTk with finite-element code written in object-oriented C++.Some significant features of EverFE include: ã The ability to model 1, 2, or 3 slab and/or shoulder units longitudinally and/or transversely (up to9 slab-shoulder units total in a 3x3 configuration). Transverse tie bars between adjacent slab-shoulder units can be explicitly modeled. ã Up to three elastic base layers with a bonded or unbonded base can be specified. Slab-base sheartransfer can be captured via an elastic-plastic distributed horizontal stiffness between the slabsand base. A tensionless or tension-supporting dense liquid foundation underlies the bottom-mostmodel layer. ã Linear or nonlinear aggregate interlock shear transfer can be simulated at transverse joints. ã Dowels can be precisely located across transverse joints, and dowel looseness modeled. In lieu of modeling dowel looseness, a dowel-slab support modulus can be specified to model dowel-slabinteraction. ã Dowel misalignment and mislocation can be modeled. ã A variety of different axle configurations can be easily defined with a minimum amount of input. ã Linear, bilinear, and trilinear thermal gradients through the slab thickness can be captured. Thisallows the simulation of thermal effects as well as slab shrinkage. ã EverFE’s extensive post-processing capabilities permit the visualization of stresses,displacements, and internal dowel forces and moments. Critical response values at any point inthe model can be easily retrieved.This manual details the finite-element implementation of EverFE, and includes descriptions of criticalfeatures and references to appropriate literature that augment the material presented here. For specificinstructions on the use of the software, see the help file EverFE_help.chm , which is integrated with the Help menu in the EverFE interface. This manual is organized into the following topics: Finite-ElementDiscretization; Modeling of Dowels and Ties; Aggregate Interlock Modeling; Treatment of Axle andThermal Loads; Finite Element Solution Strategies; and Program Architecture and File Structure. 2. Basic Finite-Element Discretization There are five elements in EverFE’s finite-element library: 20-noded quadratic brick elements areused to discretize the slab and elastic base and sub-base layers; 8-noded planar quadratic elementsincorporate the dense liquid foundation below the bottom-most elastic layer; 16-noded quadratic interfaceelements implement both aggregate interlock joint shear transfer and shear transfer at the slab-baseinterface; and 3-noded embedded flexural elements are coupled with conventional 2-noded shear beamelements to model dowels at transverse joints and ties at longitudinal joints. Figure 1 shows a finite-element mesh of a four-slab model and the corresponding elements. The flexural elements used to modeldowels and ties are detailed separately in Section 4, and aggregate interlock modeling is covered inSection 5. 2 Figure 1: Basic Finite-Element Discretization2.1 Model boundary conditions The boundary conditions are the minimum required to prevent rigid-body motion, but differ slightlydepending on whether or not an elastic base layer is explicitly modeled. In the case where a base layer ismodeled, the slabs are restrained in the horizontal x - y plane by the shear stiffness of the slab-baseinterface as discussed in Section 3, and receive vertical support from contact with the base. Rigid bodymotion of the base and sub-base layers is prevented by restricting the x - and y - displacements of one nodeon the – x face, and restricting the x -displacement of a second node on the – x face. Vertical support of theentire system is provided by the dense liquid foundation, which is always incorporated below the bottom-most layer of the model.If the slabs are founded directly on a dense liquid, i.e. no base layer is modeled, each slab isrestrained against x - and y -direction displacements at one node on its – x face, and against x -directiondisplacement at a second node on its – x face to prevent rigid-body motion of each slab. Again, verticalsupport is provided by the dense liquid foundation. 2.2 Modeling of the slab, base and sub-base layers In all EverFE models, the slab, base and sub-base layers are treated as 3D, linearly elastic, isotropiccontinua. Each layer is discretized with standard 20-noded “serendipity” brick elements. The finite-element meshes are rectilinear, and the same number of element divisions is used for each slab and thebase/sub-base layers below the slab in the x - y plane to ensure compatibility at the slab-base interface.Details of the brick element formulation and implementation can be found in finite-element textssuch as Zienkiewicz and Taylor (1994). To maintain generality, an isoparametric element formulation is 20-noded brick elementzerothickness16-noded interface element8-noded dense liquid element x y z 20-noded brick elementzerothickness16-noded interface element8-noded dense liquid element x y z 3used and all required element integration is performed numerically using 8-point (2x2x2) Gaussquadrature. The initial public release of EverFE (version 1.02, released January 1998) used 27-point(3x3x3) Gauss integration; however, subsequent internal studies showed that the higher-order integrationscheme added to the computational time without significantly improving accuracy. 2.3 Modeling of the dense liquid foundation The dense liquid foundation can either support tension, or be tensionless. It is important to note thatthe tensionless dense liquid does not account for any pre-compression due to dead load, i.e. the totalvertical deflection including the effect of dead load must be overcome before the dense liquid foundationstress and stiffness become zero.The 8-noded element illustrated in Figure 1 is used to discretize the dense liquid. This element wasformulated specifically for this application, and full details of the implementation can be found in Davids(1998). The element incorporates standard quadratic shape functions for interpolation of verticaldisplacements within the element (Zienkiewicz and Taylor 1994), ensuring that it displaces compatiblywith the 20-noded brick element with which it shares nodes. An isoparametric element formulation isused, and all necessary element integrations are performed numerically using 9-point (3x3) Guassquadrature to ensure accurate results when the tensionless option is selected.The only constitutive parameter needed for this element is the distributed stiffness of the dense liquidfoundation [force/volume]. For the tensionless foundation, if tension occurs at an element integrationpoint during the solution process, the stress and stiffness at that point are set to zero during integration of the element stiffness matrix and equivalent force vector. For the conventional, tension-supporting denseliquid, the stiffness remains constant at all points. 3. Treatment of the Slab-Base Interface Modeling interaction of the slab and base is crucial to predicting pavement response to axle loadsnear joints and to thermal or shrinkage gradients. EverFE allows the consideration of either perfect bondbetween the slab and base, or separation of the slab and base under tension. In both cases, the slab andbase do not share nodes, and nodal constraints are used to satisfy the required contact conditions (seeFigure 2). The solution algorithm relies on a perturbed Lagrangian formulation and a nodal constraint-updating scheme based on the current normal stress between the slab and base. More details on the globalnonlinear solution strategy are given in Section 7.Shear transfer between the slab and base can be important when analyzing pavements subjected tothermal and/or shrinkage strains. Rasmussen and Rozycki (2001) overviewed the factors governing slab-base shear transfer, noting that both friction and interlock between the slab and base play a role. Inaddition, they calibrated a bilinear, elastic-plastic shear transfer model from results of push tests of slabs Base elementInterfaceelements transfershear stressSlab elementPairs of nodes vertically constrainedif compression at interface x or y z x or yk SB oo Interface constitutive relationship Figure 2: Modeling Separation and Shear Transfer at the Slab-Base Interface Base elementInterfaceelements transfershear stressSlab elementPairs of nodes vertically constrainedif compression at interface x or y z x or yk SB oo Interface constitutive relationship Figure 2: Modeling Separation and Shear Transfer at the Slab-Base Interface
