# Doing the Math

Thanks to a grant from the ICPI Foundation for Education and Research, design tables were developed earlier this year that provide technically conservative base solutions for paving slabs subject to vehicles. The tables were developed using finite element modeling that simulated pressures from truck tires on paving slabs of various sizes and flexural strengths. The modeling included a 1-inch (25 mm) thick sand bed under the slabs, three base materials, and three soil subgrade conditions. This article previews the design approach for pedestrian and vehicular applications derived from that modeling.

For pedestrian applications, 12 x 12 in. (300 x 300 mm) units can be placed on a minimum 6 in. (150 mm) thickness of compacted aggregate base. Thicker bases (generally 8 to 12 in. or 200 to 300 mm thick) should be used in freezing climates and/or on weak clay soils (CBR < 3%). Designers should consider using a lean concrete or concrete base for larger paving units because achieving a very smooth base surface can be difficult with compacted aggregate base.

Design options become a bit more complex for vehicular applications. The first step is determining the maximum number of lifetime 18,000 lb equivalent single axle load or ESAL repetitions. (Caltrans Traffic Indexes are provided in parentheses.) Determining ESALs or TIs can be done using Table 1. It divides them into five categories. Higher ESAL categories generally require thicker units and concrete bases. Applications exceeding 75,000 lifetime ESALs should use interlocking concrete pavers.

The next step is determining the soil strength. The minimum values for designs is a resilient modulus of 5,100 psi (35 MPa), 3% California Bearing Ratio, or an R-value = 7. The maximum values are 11,600 psi (80 MPa), 10% and 18, respectively. Soils with higher values use the latter set for determining the unit size and thickness. after laboratory tests determine the soil strength, that points to specific slab sizes and bases that will work given the anticipated design ESALs in Table 2. Square paving units are recommended over rectangular ones for vehicular traffic with placement in a running bond pattern.

The ICPI design method offers three base options described below in ascending order of supporting stiffness. Construction should include compacting the soil subgrade and bases/subbases to at least 95% of standard Proctor density per ASTM D698 *Standard Test Methods for Laboratory Compaction of Soil Standard Effort*.

(a) A 12 in. (300 mm) thick compacted aggregate base with gradation conforming to provincial, state or municipal specifications for road base used under asphalt pavement. If there are no guidelines, use the gradations in ASTM D2940 *Standard Specification for Graded Aggregate Material for Bases or Subbases for Highways or Airports* and as described in ICPI Tech Spec 2 *Construction of Interlocking Concrete Pavements*.

(b) A 4 in. (100 mm) thick lean concrete base over a 6 in. (150 mm) thick compacted aggregate base. The lean concrete should have a minimum 725 psi (5 MPa) compressive strength after 7 days per ASTM D1633 *Standard Test Methods for Compressive Strength of Molded Soil-Cement Cylinders*. Lean concrete is typically a lower strength concrete or a cement-treated base of similar stiffness and strength where an aggregate base is charged with cement (typically 3% to 6% by weight) to bind the aggregates when the cement cures.

(c) A 4 in. (100 mm) thick concrete base over a 6 in. (150 mm) compacted aggregate base. The concrete should have a minimum compressive strength is 3,000 psi (20 MPa) per ASTM C39 *Standard Test Method for Compressive Strength of Cylindrical Concrete Specimens*.

Table 2 presents a sample of the design tables using a concrete base. The designer finds the paving slab length and width and thickness that corresponds to the soil subgrade strength and slab flexural strength. Paving slab length and widths start at 12 x 12 in. and go up to 48 x 48 in. As an illustrative example, Table 2 only goes to 24 in. slabs and not up to 48 in. due to space limitations. Slab thicknesses are 2, 3, 4 and 5 in. If the exact paving slab length and width are not on the table, the designer finds the closest size paving slab, using a smaller and/or thicker unit as a conservative design measure. The design tables cover square and rectangular slabs only.

An example follows on how a design table works. The highlighted 24 x 24 x 3 in. thick slab is selected by the designer. This will be a concrete base and aggregate subbase over a 5% CBR subgrade with a minimum 750 psi flexural strength for the slabs. The intersection of the highlighted horizontal and vertical columns is marked OHV which means the maximum lifetime load is 75,000 ESALs per Table 1. If the designer wants to use a 24 x 24 x 3 in. slab on a weaker soil subgrade, then the maximum allowed ESALs would be 30,000.

Designs using a concrete base include a 1 in. (25 mm) thick sand setting bed under the slabs. This design solution also applies to paving slabs in a bitumen-sand bed (typically 1 in. or 25 mm thick) since bitumen-set applications require a concrete base. This introduces an additional measure of conservative design since bitumen-sand materials provide a modest increase in stiffness and increased stability resisting repeated turning, accelerating, and braking tire lateral loads.

This article was intended to sample how structural design is done with paving slabs. Similar, additional design tables have been developed for planks and an ICPI Tech Spec is expected later in 2017. As partial validation, the ICPI Foundation for Education and Research is funding the construction of a full-scale load testing area at a paver manufacturing facility in Maryland. The area will receive trucks loaded with paving products where each truck pass will exert several ESALs. The condition of the slabs and planks set on aggregate and concrete bases will be monitored to see how quickly or slowly the slabs will crack, as that defines failure. The testing will likely begin in spring 2017 and run for a few years.