Serviceability, Overlay Design and Concrete Moduli: 16-Civ-B7 Transportation Planning and Engineering, May 2016, Q7

Question 7: Serviceability, Overlay Design and Concrete Moduli (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.

Given.

Quantity	Symbol	Value
Original design period / overlay period	—	20 years / a further 15 years
Existing asphalt concrete	D₁, a₁	100 mm, 0.32
Existing roadbase	D₂, a₂	300 mm, 0.10
Existing subbase	D₃, a₃	400 mm, 0.08
Future (required) structural number	SN_f	120 mm
Layer coefficient of the new asphalt	a_ol	0.42
Concrete compressive strength	f′_c	5000 psi (34.5 MPa)

Find. (a) a serviceability-versus-time diagram covering the original design period, the overlay and the subsequent service life; (b) the effective structural number of the existing pavement and the asphalt overlay thickness needed to reach the future structural number; (c) estimates of the modulus of rupture and modulus of elasticity of the concrete.

Approach. Part (a) is answered directly by the sketch below. Part (b) uses the structural-number summation in the millimetre convention the question itself adopts (the future SN is quoted as 120 mm), takes the difference between future and effective values, and divides by the new layer's coefficient. Part (c) applies the standard empirical square-root relations between compressive strength and the two moduli.

Part (a) — effect of traffic and of an overlay on serviceability. A new flexible pavement opens at an initial present serviceability index of roughly 4.2 to 4.5 and loses serviceability slowly at first, then increasingly quickly as fatigue cracking, rutting and roughness accumulate; the design period ends when the curve reaches the terminal serviceability, here taken as 2.5, after twenty years. An asphalt overlay placed at that point restores both ride quality and structural capacity, lifting the curve almost back to its original level, after which it decays again under the following fifteen years of traffic. The second decay is generally steeper than the first, because the overlay inherits the distress and the reflective cracking of the pavement beneath it.

Answer to part (a): serviceability against time. The original pavement decays from its initial PSI to the terminal value over the 20-year design period; the overlay restores serviceability and structural capacity, and the pavement then decays again, more steeply, over the following 15 years.

Part (b) — effective structural number of the existing pavement. The question quotes the future structural number as 120 mm, so the millimetre convention is used throughout and thicknesses enter directly in millimetres: $$SN_{\text{eff}} = \sum a_iD_i = 0.32(100) + 0.10(300) + 0.08(400)$$ The contributions are 32, 30 and 32 mm respectively, so $$\boxed{SN_{\text{eff}} = 94\ \text{mm}}$$ The layer coefficients here are notably lower than those of new materials — 0.32 against 0.42 for the asphalt — which is exactly what a condition survey does: it discounts each layer for the distress observed in it.
Structural number the overlay must supply. The overlay makes up the difference between what the pavement must have and what it still has: $$SN_{ol} = SN_f - SN_{\text{eff}} = 120 - 94 = 26\ \text{mm}$$
Convert that to an asphalt thickness. Dividing by the layer coefficient of the new asphalt, $$D_{ol} = \frac{SN_{ol}}{a_{ol}} = \frac{26}{0.42} = 61.9\ \text{mm}$$ $$\boxed{D_{ol} = 62\ \text{mm}, \text{ specify } 65\ \text{mm}}$$ Sixty-five millimetres is also sensible on constructability grounds: it is roughly two-and-a-half times the nominal maximum aggregate size of a typical surface mix, so it can be placed and compacted in a single lift. A 50 mm overlay would supply only 21 mm of structural number and leave the pavement short.
Part (c) — modulus of rupture. The flexural tensile strength of concrete is estimated from its compressive strength by $$f_r = 7.5\sqrt{f'_c} = 7.5\sqrt{5000} = 7.5(70.71)$$ $$\boxed{f_r = 530\ \text{psi} \; (3.66\ \text{MPa})}$$ This is the ACI 318 value. For rigid pavement design specifically, AASHTO and the Portland Cement Association use a coefficient between 8 and 10, which brackets the same strength between 566 and 707 psi; a design value of 650 psi (4.5 MPa) would be usual for a pavement-quality concrete of this strength. The Canadian expression, $f_r = 0.62\sqrt{f'_c}$ with both quantities in MPa, gives $0.62\sqrt{34.5} = 3.64$ MPa — the same answer, since the two forms are the same relation in different units.
Modulus of elasticity. For normal-density concrete, $$E_c = 57\,000\sqrt{f'_c} = 57\,000\sqrt{5000} = 57\,000(70.71)$$ $$\boxed{E_c = 4.03\times10^{6}\ \text{psi} \; (27.8\ \text{GPa})}$$ The Canadian form for normal-density concrete, $E_c = 4700\sqrt{f'_c}$ in MPa, gives $4700\sqrt{34.5} = 27\,600$ MPa, confirming the same result. Both are empirical fits that assume a normal-density aggregate near 2400 kg/m³; a lightweight or unusually stiff aggregate can move the true modulus by 20 per cent or more, which is why a measured value is preferred whenever deflections govern.

Quantity	Result
(b) Effective structural number, SN_eff	94 mm (32 + 30 + 32)
Structural number required of the overlay	26 mm
Required overlay thickness	61.9 mm — specify 65 mm
(c) Modulus of rupture, f_r (ACI, 7.5√f′_c)	530 psi = 3.66 MPa
Modulus of rupture, pavement range (8–10√f′_c)	566–707 psi (adopt 650 psi)
Modulus of elasticity, E_c	4.03 × 10⁶ psi = 27.8 GPa

Topic. Present serviceability over a pavement's life, structural-deficiency overlay design, and empirical strength–modulus relations for concrete.

Key relations. $SN_{\text{eff}}=\sum a_iD_i$ (millimetre convention, $SN_{mm}=25.4\,SN_{in}$); $SN_{ol}=SN_f-SN_{\text{eff}}$; $D_{ol}=SN_{ol}/a_{ol}$; $f_r = 7.5\sqrt{f'_c}$ psi $=0.62\sqrt{f'_c}$ MPa; $E_c = 57\,000\sqrt{f'_c}$ psi $=4700\sqrt{f'_c}$ MPa.

Why this works. The serviceability concept converts a subjective judgement — how good does this road feel to drive — into a number that decays monotonically with traffic, and it is that decay curve, not any single distress, which defines the end of a design period. Overlay design in the AASHTO framework is then simply arithmetic on the same index used for new construction: a condition survey assigns reduced layer coefficients that reflect the distress actually observed, the resulting effective structural number measures what the pavement can still do, and the deficiency is made up in the stiffest material available. Working the whole calculation in millimetres, as this question does, changes nothing but the units — the layer coefficients are dimensionless, so a structural number in millimetres is exactly 25.4 times the same number in inches. For concrete, both moduli scale with the square root of compressive strength because all three properties trace back to the same paste quality; the relations are empirical fits, not derivations, which is why the coefficient for the modulus of rupture varies between codes and applications.

Common pitfall. Mixing the two structural-number conventions — converting the layer coefficients when moving between inches and millimetres. The coefficients are unchanged; only the thicknesses carry units. A second error is reading the 120 mm future structural number as a required thickness, which it is not: 120 mm of structural number corresponds here to well over half a metre of pavement. A third is treating the modulus of rupture as if it were a single defined constant when the coefficient depends on the code and the application.

Source. AASHTO, Guide for Design of Pavement Structures (1993), Part III Ch. 5 (rehabilitation with overlays) and Appendix on serviceability; TAC, Pavement Asset Design and Management Guide, Ch. 6 (condition assessment and rehabilitation); CSA A23.3-19, §8.6 (modulus of rupture and modulus of elasticity); Mamlouk & Zaniewski, 4th ed., Ch. 7 (portland cement concrete).

Question 7 of 7: Serviceability, Overlay Design and Concrete Moduli

Question 7: Serviceability, Overlay Design and Concrete Moduli (20 marks)