## Design

### Questions:

#### How are back calculated moduli adjusted for in-service conditions?

#### What are suitable moduli to use for unbound granular M/4 overlays?

#### What are suitable moduli to use for bound overlays?

### Answers:

#### How are back calculated moduli adjusted for in-service conditions?

Because the moduli of granular layers are stress dependent, an adjustment to back-calculated moduli is required if the stresses imposed at the time of testing are significantly different from those that will be applied in service conditions. ARRB (1994) recommend the following adjustments:

Ei-s = Ei-m * (in-service mean stress / measurement mean stress)K

where:

Ei-s is the modulus of granular layer i for the in service condition

Ei-m is the modulus as measured

K is a constant selected from the range 0.3 (low quality sub-base material) to 0.5 (high quality basecourse material)

The stresses at the mid-depth of each layer need to be obtained from the analysis and an appropriate correction applied. If the loading used for measurement is equal to (or slightly less than) the in service stress, then no correction is required (or minimal conservatism results.)

Where non-linear elastic subgrade moduli have been approximated in a sub-layering process (eg EFOMD2/CIRCLY), the moduli should be adjusted as follows for the forward calculation (ARRB, 1994):

Ei-s = Ei-m * (300MPa - in-service deviatoric stress) / (300MPa - measurement deviatoric stress)P

where:

Ei-s is the modulus in MPa of subgrade sub-layer i for the in service condition

Ei-m is the modulus in MPa as measured

K is a function of subgrade CBR (see table below)

Subgrade CBR | P |

2 | 8 |

3 | 6 |

4 | 5 |

5 | 4 |

7 | 2 |

10 | 0.5 |

15 | 0 |

For a program where the subgrade moduli are backcalculated as stress-dependent non-linear materials (eg ELMOD) the forward analysis uses the same modulus/stress relationship with the calculated exponent for that test point. (ELMOD carries this out automatically as it combines both back and forward analysis in the one program.)

If a linear elastic program forward analysis progam such as CIRCLY is to be used with stress dependent moduli (eg from ELMOD), then the standard set of subgrade sub-layers (Section ???) should be used, the in-service stresses calculated, then the equivalent linear elastic modulus for each sublayer determined.

#### What are suitable moduli to use for unbound granular M/4 overlays?

The resilient moduli of various overlay materials are given in the AUSTROADS Pavement Design Guide, Table 6.4.

Local research, has found that these values are realistic design values for thin pavements on soft subgrades but may be somewhat conservative for stiff pavements. Unbound granular overlays produce moduli which are consistent with the AUSTROADS suggested values when first constructed, but where strains in the underlying layers are small, basecourse moduli may increase by 50% after in situ densification from trafficking.

The New Zealand Supplement (Transit, 1997) requires that the modulus used for an unbound granular overlay shall be the same as the modulus determined for the top basecourse layer. This assumption is reasonable as for stiff pavement structures a higher modulus for the unbound granular material will be used. Also the overlay modulus should not be less than the underlying existing basecourse modulus.

#### What are suitable moduli to use for bound overlays?

Alternative rehabilitation treatments such as asphaltic overlay or cement stabilisation of the basecourse layer are considered by modelling the pavement with appropriate parameters (AUSTROADS, 1992 Table 6.4b; NZ Supplement 1997). The moduli of cement stabilised basecourses used in New Zealand have been found to be highly variable. Further details on mechanistic design and modelling of rehabilitation treatments with worked examples are given by ARRB (1994), NZIHT (1996), Wardle (1980) and RTA (1994).