Question 7 of 7: Frost action, TAC typical design and a granular base equivalency alternative

Question 7: Frost action, TAC typical design and a granular base equivalency alternative (20 marks)

Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.

(a) Frost-heave action and its control. Frost heave is not the freezing of the water already in the soil — that would raise the surface by only about 9 % of the pore volume. It is the growth of segregated ice lenses fed by water drawn upward from below. Three conditions must coexist: a freezing front penetrating into the subgrade, a frost-susceptible soil, and a source of water within capillary reach. As the freezing front advances, water in the finest pores remains unfrozen as a thin adsorbed film. The curvature of the ice-water interface in those pores lowers the pressure in the film, and the resulting suction pulls further water up from the water table to the base of the ice lens, where it freezes and thickens the lens. Because the supply is essentially unlimited while the soil stays wet, heaves of 50 to 150 mm are ordinary and are almost always differential, so the road surface distorts, longitudinal and transverse cracks open and the ride deteriorates.

Susceptibility is a matter of pore size. Clean sands and gravels have pores too large to sustain the suction and do not heave; clays have pores so fine that the permeability is too low to feed a lens quickly. The worst materials are silts and silty, fine-grained soils in between — conventionally those with more than about 3 % by mass finer than 0.02 mm. The CL subgrade in this question is squarely frost susceptible, which is why the paper imposes a 600 mm minimum thickness.

The second and often more damaging phase is thaw weakening. Thawing proceeds from the surface down, so the melt water is trapped above the still-frozen soil below. Pore pressures rise, effective stress collapses, and the subgrade resilient modulus can fall to a third of its summer value for several weeks — exactly when the road is carrying its normal traffic. Spring load restrictions exist for that reason.

Countermeasures fall into four groups, and a real design usually combines them. Insulate by thickness: carry enough non-frost-susceptible granular material that the freezing front stops above the susceptible soil, or at least deep enough that the residual heave is uniform — this is the design rule the question applies as a 600 mm minimum, commonly set at 50 to 70 % of the design frost depth. Cut off the water: lower the water table with subdrains, raise the grade line on fill, seal the surface and shoulders, and provide a free-draining subbase with a positive outlet, since a lens cannot grow without a water supply. Remove or improve the soil: sub-excavate and replace the worst pockets, or stabilise them with lime or cement so the pore structure no longer sustains suction. Manage the transitions and the thaw: taper subgrade changes and structure approaches over 10 to 20 m so any residual heave is gradual rather than a bump, insulate locally with extruded polystyrene board where depth is constrained, and impose spring load restrictions during the thaw-weakened period.

(b) TAC typical design for the site.

Given. A new two-lane secondary rural highway in Ontario for a cumulative 600,000 ESALs on a frost-susceptible CL subgrade of CBR around 6, with a minimum total thickness of 600 mm.

Find. The layer thicknesses from the TAC table of typical provincial designs.

1. Choose the right table. Page 13 gives typical thicknesses at cumulative ESALs of 0.5, 1 and 10 million. The design traffic of 600,000 sits just above the first table; the nearest tabulated design is the 0.5 × 10⁶ table, and the interval to 1 × 10⁶ is used below as a sensitivity check rather than as the design.
2. Choose the right row. The three subgrade rows are keyed to soil class and CBR. The site is CL with CBR about 6, which matches the middle row, “Medium” glacial till, CBR = 5, group index 10 to 12, Unified Soil Class CL — a slightly conservative match, since the site CBR is marginally better than the tabulated 5.
3. Read the Ontario column. For that row and table, the Ontario practice is $$\text{asphalt concrete } 90\ \text{mm},\quad \text{granular base } 150\ \text{mm},\quad \text{granular subbase } 450\ \text{mm}$$ $$\boxed{\text{total} = 90 + 150 + 450 = 690\ \text{mm}}$$ which agrees exactly with the printed Ontario total of 690 mm for that row — a useful check that the column has been read correctly on a crowded table.
4. Check the frost requirement. The stated minimum is 600 mm and the TAC section provides 690 mm, so the typical design satisfies the frost criterion with 90 mm to spare. No thickening is required. (Reading the 1 × 10⁶ table instead would give 130/150/430 mm for a total of 710 mm, so the design is not sensitive to which side of 600,000 ESALs the traffic falls on.)

(c) A granular base equivalency alternative.

Given. The section from part (b), the Ontario layer equivalency ratios from appendix page 14, and a local economy in which subbase aggregate is scarce and expensive while asphalt is cheap.

Find. An alternative section of equal structural worth that uses as little subbase as possible while still meeting the 600 mm frost minimum.

1. State the equivalency ratios. Appendix page 14 gives, for Ontario, 2.00 for asphalt concrete, 1.80 for a Portland-cement-treated base, 1.50 for an asphalt-treated base, 1.00 for granular base and 0.67 for granular subbase. Each ratio says how many millimetres of granular base one millimetre of that material replaces.
2. Express the reference design as a granular base equivalency. $$GBE_{ref} = 90(2.00) + 150(1.00) + 450(0.67) = 180 + 150 + 301.5 = \boxed{631.5\ \text{mm}}$$ Any alternative must reach at least this equivalency to be structurally equal.
3. Set up the trade. Keep the granular base at its practical minimum of 150 mm (it is the working platform for paving) and let the asphalt thickness be t₁ and the subbase t₃. Two constraints apply: $$\text{frost:}\ \ t_1 + 150 + t_3 \ge 600, \qquad \text{structure:}\ \ 2.00\,t_1 + 150 + 0.67\,t_3 \ge 631.5$$ Because subbase is the expensive material, the optimum sits where both constraints are tight. Substituting $t_3 = 450 - t_1$ from the frost constraint into the structural constraint, $$2.00\,t_1 + 150 + 0.67(450 - t_1) \ge 631.5 \quad\Longrightarrow\quad 1.33\,t_1 \ge 119.7 \quad\Longrightarrow\quad t_1 \ge 135.3\ \text{mm}$$
4. Adopt buildable thicknesses. Rounding the asphalt up to a constructible 140 mm (two 70 mm lifts, or a 90 mm binder and a 50 mm surface) and taking the balance of the 600 mm in subbase, $$\boxed{\text{asphalt concrete } 140\ \text{mm},\quad \text{granular base } 150\ \text{mm},\quad \text{granular subbase } 310\ \text{mm}}$$
5. Verify the alternative. Structurally, $$GBE_{alt} = 140(2.00) + 150(1.00) + 310(0.67) = 280 + 150 + 207.7 = \boxed{637.7 \ge 631.5\ \text{mm}}$$ and the total thickness is exactly 600 mm, meeting the frost minimum. The scarce subbase falls from 450 mm to 310 mm, a saving of 140 mm or 31 % of the subbase quantity, paid for with an extra 50 mm of asphalt from a plant next door.
6. Comment on what the trade actually costs. The exchange is favourable only because the two constraints pull in the same direction here: asphalt is worth twice its thickness structurally, so replacing subbase with asphalt reduces total thickness, and the binding limit becomes frost rather than structure. Three practical points belong in the answer. First, the alternative sits exactly on the 600 mm frost minimum, so there is no slack — if the frost design depth were revised upward, subbase would have to come back. Second, thicker asphalt on a secondary rural road is more vulnerable to low-temperature transverse cracking and costs far more per cubic metre than granular material, so the economic case rests entirely on the stated local haul advantage and should be tested with an actual unit-rate comparison. Third, an asphalt-treated base at a ratio of 1.50 is worth examining as a middle option: 150 mm of asphalt-treated base is worth 225 mm of granular base while remaining cheaper per cubic metre than a surface-quality mix, and it would let the granular subbase be trimmed without a 140 mm asphalt surface.