Modular ratios for unbound granular pavement layers

Unbound granular pavement layers show a characteristic increase in moduli from the subgrade to the surface. The ratio of moduli between successive layers provides a direct and effective measure of pavement quality that makes due allowance for site conditions and seasonal effects beyond a contractor’s control. The modular ratio is therefore an effective indicator for performance-based specifications. Modular ratios are readily determined from backanalysis of Falling Weight Deflectometer bowls recorded during construction monitoring or long-term structural condition studies. Their applications to new construction quality assurance and performance-based network maintenance contracts are described. Dorman and Metcalf (1965) used the concept of modular ratio limitations in successive unbound layers to propose the relationship: Ei / Ei+1 = 0.2 hi 0.45 and 2 < Ei / Ei+1 < 4 (1) where hi is the height of the overlying layer in mm. Subsequently, Brown and Pappin (1985) found (using more rigorous non-linear finite element analyses) that the above limitations were too restrictive, and reported: 1.5 < Ei / Ei+1 < 7.5 (2) For mechanistic design, AUSTROADS (1992, 2004) recommends sub-layering of granular materials placed directly on the subgrade with constraints that the sub-layer thickness must be approximately in the range of 50-150 mm, and that the ratio of moduli of adjacent sub-layers does not exceed 2. Moffat & Jameson (1998a) used sub-layering in multi-layer linear elastic models to refine the original AUSTROADS procedures for mechanistic design of new unbound granular pavements and proposed the following: (a) Divide the granular materials into 5 layers of equal thickness (b) Adopt the vertical modulus for the top sub-layer from: Ev top of base = Ev subgrade x 2 granular thickness/125) (3) (but not exceeding tabulated upper bounds for the materials) (c) Determine the modular ratio of successive sub-layers from: R = [Ev top of base / Ev subgrade] 1/5 (4) (d) Calculate the modulus of each layer beginning with that immediately overlying the subgrade of known modulus Moffat and Jameson (1998b) recommend upper bounds for unbound granular moduli of 500 MPa (high standard) or 350 MPa (normal standard) under thin surfacings subject to standard axle loadings. Thicker surfacings, providing more effective loadspread, result in reduced values owing to the stress dependence of unbound layer moduli. The moduli presented assume anisotropy with the vertical modulus twice the horizontal modulus in each layer. The above relationships are intended for forward design. However back-analysed moduli (viz. from Falling Weight Deflectometer surveys) should be checked using the above criteria to check that a reasonable pavement model has been obtained when carrying out sensitivity analyses with respect to varying layer thicknesses. Clearly, only unbound layer moduli are restricted in this manner as the moduli of bound materials are influenced much less by the stiffness of underlying layers. II COMPARISON OF RELATIONSHIPS The Moffat and Jameson procedure can be transformed to show the effect of layer thickness explicitly allowing direct comparison with the Dorman and Metcalf relationship as shown in Figure 1. The transformation also allows the same principle to be adapted to layers of differing thickness (generally encountered in existing pavements) which will be discussed below in relation to back analysis of deflection results.