Materials

5% of exam

Mix design of concrete and asphalt, test methods and specifications, and physical and mechanical properties of metals, concrete, aggregates, asphalt, and wood.

3 concepts

Exam areas

A. Mix design of concrete and asphalt

Mix Design of Concrete and Asphalt

Proportion concrete by absolute volume around the water-cement ratio, and design asphalt by volumetrics to an optimum binder content — the two materials problems the FE Civil rewards most.

Mix design is where civil materials stops being descriptive and becomes a calculation: you are handed performance targets — a strength, a slump, a durability class for concrete; an air-void content and traffic level for asphalt — and you must return a recipe in pounds (or kilograms) per unit volume. The FE Reference Handbook's Materials Science chapter gives you the one fact that anchors all of concrete proportioning — that strength falls as the water-cement ratio rises; the absolute-volume bookkeeping that turns that fact into a batch is the ACI 211.1 procedure. Points are lost when candidates confuse mass proportions with volume proportions, forget that entrained air occupies real volume, or treat asphalt binder content as a mass fraction when the design criterion is a volume of air voids. Get the two accounting systems straight — mass for the water-cement ratio, volume for the batch — and these problems become arithmetic.

Water-cement ratio drives strength

The single most important number in a concrete mix is the water-cement ratio

w/c

, the mass of mixing water divided by the mass of cementitious material. Lower

w/c

means less capillary porosity in the hardened paste and therefore higher compressive strength and better durability — the handbook's strength-versus-

w/c

chart shows

28

-day strength climbing steeply as

w/c

drops from

0.80

toward

0.40

. Abrams' law captures the trend as an inverse-exponential relation. You select

w/c

as the smaller of the value the target strength requires and the value the exposure (freeze-thaw, sulfates, chlorides) permits, then never exceed it.

w/c = \dfrac{W_{water}}{W_{cement}}, \qquad f'_c = \dfrac{A}{B^{\,w/c}}

The absolute-volume method

A batch must fill a known volume —

27\ \text{ft}^3

in one cubic yard, or

1\ \text{m}^3

in SI — so proportioning is a volume balance. Each ingredient's absolute volume is its mass divided by its density, where density is the specific gravity times the unit weight of water (

62.4\ \text{lb/ft}^3

1000\ \text{kg/m}^3

). Add the absolute volumes of cement, water, air, and coarse aggregate; whatever volume remains to reach the total is filled by fine aggregate, whose mass you back-calculate. Air is not free space you can ignore — entrained and entrapped air occupy a real fraction of the volume and must be entered into the balance.

V_i = \dfrac{W_i}{SG_i\,\gamma_w}, \qquad \sum V_i = V_{cement}+V_{water}+V_{air}+V_{CA}+V_{FA} = V_{total}

Slump and workability

Slump is the field measure of workability: a higher slump is a wetter, more fluid mix that places more easily but, if achieved by simply adding water, raises

w/c

and sacrifices strength. The correct way to gain workability without water is a water-reducing admixture or a superplasticizer, which disperses the cement and frees up water already in the mix. Workability also depends on aggregate gradation and the paste volume. Typical placements call for

1

4\ \text{in}

of slump; pavements run stiffer, heavily reinforced sections wetter.

\text{add water} \Rightarrow \uparrow\text{slump} \;\text{but}\; \uparrow w/c \Rightarrow \downarrow f'_c

Air entrainment for durability

Deliberately entrained air — millions of tiny, stable bubbles created by an air-entraining admixture — gives freezing water somewhere to expand, dramatically improving freeze-thaw durability. The handbook notes air entrainment is used to improve durability, with a typical target of

4

7\%

by volume depending on aggregate size and exposure. There is a tradeoff: each percent of air costs roughly

5\%

of compressive strength, but it also improves workability, letting you trim water. In the absolute-volume balance, air enters as a volume equal to the air percentage times the total batch volume.

V_{air} = (\text{air fraction})\times V_{total}

Asphalt mix design — Superpave and Marshall

Hot-mix asphalt is designed by volumetrics, not strength. You compact specimens at several binder contents — in a Superpave gyratory compactor to a design gyration count

N_{des}

, or with Marshall hammer blows in the older method — and measure three void parameters. Air voids (

V_a

or VTM) are the empty volume in the compacted mix; voids in the mineral aggregate (VMA) are the inter-granular space filled by binder plus air; voids filled with asphalt (VFA) is the fraction of VMA occupied by effective binder. These come from the bulk specific gravity of the compacted mix

G_{mb}

, the maximum (void-free) specific gravity

G_{mm}

, and the bulk specific gravity of the aggregate

G_{sb}

V_a = 100\!\left(1-\dfrac{G_{mb}}{G_{mm}}\right), \quad VMA = 100\!\left(1-\dfrac{G_{mb}\,P_s}{G_{sb}}\right), \quad VFA = 100\,\dfrac{VMA-V_a}{VMA}

Optimum binder content

The design asphalt content is the binder content that yields a target air-void content — universally

4.0\%

for Superpave dense-graded mixes — provided VMA and VFA also satisfy their minimums for the chosen nominal maximum aggregate size and traffic level. You plot each measured property against binder content, read the binder content that gives exactly

4\%

air voids, and confirm the other criteria are met there. Too little binder leaves high voids and a brittle, permeable mat; too much closes the voids, lowers stability, and invites rutting and bleeding. The Marshall method likewise takes optimum at the design air-void content — historically the average of the binder contents at maximum stability, maximum unit weight, and the median (

4\%

) of the design air-void range — so the volumetric, not the stability-peak, criterion governs.

P_{b,opt} = P_b \;\text{such that}\; V_a = 4.0\%

Exam strategy

Keep two ledgers. For the water-cement ratio work in mass; for the batch work in absolute volume, and convert with

V=W/(SG\,\gamma_w)

. The classic concrete question gives cement mass,

w/c

, air percent, and coarse-aggregate mass and asks for sand mass — solve it by filling

27\ \text{ft}^3

: sum the known absolute volumes (don't forget air), subtract from total, and convert the leftover volume back to sand mass. For asphalt, memorize the three void definitions and that optimum binder content is set at

4\%

air voids; watch whether

P_s = 1-P_b

is wanted as a decimal or a percent, and never compute VMA with

G_{mm}

— VMA uses the aggregate bulk specific gravity

G_{sb}

Key equations

Water-cement ratio

w/c = \dfrac{W_{water}}{W_{cement}}

Mass of mixing water over mass of cementitious material (dimensionless). The primary determinant of concrete strength and durability; lower is stronger.

Abrams' strength law

f'_c = \dfrac{A}{B^{\,w/c}}

Empirical inverse-exponential drop of 28-day strength $f'_c$ with $w/c$ ; $A$ , $B$ are material constants. Captures the handbook strength-vs- $w/c$ trend.

Absolute volume of an ingredient

V_i = \dfrac{W_i}{SG_i\,\gamma_w}

Solid volume occupied by mass $W_i$ ; $SG_i$ = specific gravity, $\gamma_w=62.4\ \text{lb/ft}^3$ ( $1000\ \text{kg/m}^3$ ). Foundation of mix proportioning.

Volume balance (batch)

V_{cement}+V_{water}+V_{air}+V_{CA}+V_{FA}=V_{total}

Absolute volumes must fill the batch volume ( $27\ \text{ft}^3$ per yd $^3$ or $1\ \text{m}^3$ ). Solve for the unknown ingredient (usually fine aggregate).

Air volume

V_{air}=(\text{air fraction})\,V_{total}

Entrained plus entrapped air as a real volume; e.g., $5\%$ of $27\ \text{ft}^3 = 1.35\ \text{ft}^3$ . Must be included in the balance.

Concrete yield / unit weight

\gamma_{concrete}=\dfrac{\sum W_i}{V_{total}}

Total batch mass over total volume gives fresh unit weight (typ. $\approx 145\ \text{lb/ft}^3$ normalweight). Used to check the design and compute yield.

Asphalt air voids (VTM)

V_a = 100\!\left(1-\dfrac{G_{mb}}{G_{mm}}\right)

Percent air in the compacted mix; $G_{mb}$ = bulk SG of compacted specimen, $G_{mm}$ = maximum (rice) SG. Design target $4.0\%$ .

Voids in mineral aggregate (VMA)

VMA = 100\!\left(1-\dfrac{G_{mb}\,P_s}{G_{sb}}\right)

Inter-granular void space (binder + air) as percent of total volume; $P_s=1-P_b$ = aggregate mass fraction, $G_{sb}$ = aggregate bulk SG. Has a minimum by NMAS.

Voids filled with asphalt (VFA)

VFA = 100\,\dfrac{VMA-V_a}{VMA}

Percent of VMA occupied by effective binder. Has both a minimum and maximum tied to traffic level.

Effective specific gravity of aggregate

G_{se}=\dfrac{100-P_b}{\dfrac{100}{G_{mm}}-\dfrac{P_b}{G_b}}

Aggregate SG including pores not filled by binder; $P_b$ = binder percent by total mass, $G_b$ = binder SG ( $\approx1.02$ ). Lies between $G_{sb}$ and apparent SG.

Binder content by total mass

P_b = \dfrac{W_{binder}}{W_{mix}}\times100

Asphalt content as a percent of total mix mass (binder + aggregate). The design variable optimized to hit $4\%$ air voids.

Optimum binder content

P_{b,opt}=P_b\big|_{V_a=4.0\%}

Binder content giving exactly $4.0\%$ design air voids, provided VMA and VFA criteria are also satisfied there.

Worked examples

Absolute-volume proportioning of one cubic yard

Problem. Design $1\ \text{yd}^3$ ( $27\ \text{ft}^3$ ) of normalweight concrete. Cement content is $564\ \text{lb}$ ( $SG=3.15$ ), the water-cement ratio is $0.45$ , target entrained air is $5\%$ , and the coarse aggregate is $1800\ \text{lb}$ ( $SG=2.68$ ). Fine aggregate has $SG=2.63$ . Find the required water and the required fine-aggregate mass, then check the unit weight.

Solution. Work cement and water in mass, the batch in absolute volume; use

\gamma_w=62.4\ \text{lb/ft}^3

. Water mass:

W_w=(w/c)\,W_c=0.45\times564=253.8\ \text{lb}

. Absolute volumes:

V_{cem}=564/(3.15\times62.4)=2.869\ \text{ft}^3

;

V_{water}=253.8/62.4=4.067\ \text{ft}^3

;

V_{air}=0.05\times27=1.350\ \text{ft}^3

;

V_{CA}=1800/(2.68\times62.4)=10.763\ \text{ft}^3

. Sum of knowns

=2.869+4.067+1.350+10.763=19.050\ \text{ft}^3

, so fine-aggregate volume

=27-19.050=7.950\ \text{ft}^3

. Fine-aggregate mass

=V_{FA}\,SG\,\gamma_w=7.950\times2.63\times62.4=1305\ \text{lb}

\boxed{W_w=254\ \text{lb},\ W_{FA}=1{,}305\ \text{lb}}

(3 sig figs). Sanity check: total mass

=564+254+1800+1305=3{,}923\ \text{lb}

, so unit weight

=3923/27=145\ \text{lb/ft}^3

— exactly the expected normalweight value, confirming the volume balance closes.

V_{FA}=27-\sum V_{known}=7.95\ \text{ft}^3 \;\Rightarrow\; W_{FA}=7.95(2.63)(62.4)=1{,}305\ \text{lb}

Asphalt volumetrics: air voids, VMA, and VFA

Problem. A Superpave specimen has bulk specific gravity $G_{mb}=2.441$ and the loose mix has maximum specific gravity $G_{mm}=2.535$ . The aggregate bulk specific gravity is $G_{sb}=2.705$ and the binder content is $P_b=5.0\%$ by total mass. Compute the air voids, VMA, and VFA, and state whether this specimen is at the design air-void target.

Solution. Aggregate mass fraction:

P_s=1-P_b=1-0.05=0.95

. Air voids:

V_a=100(1-G_{mb}/G_{mm})=100(1-2.441/2.535)=100(1-0.9629)=3.71\%

. VMA:

VMA=100(1-G_{mb}P_s/G_{sb})=100\!\left(1-\dfrac{2.441\times0.95}{2.705}\right)=100(1-0.8573)=14.27\%

. VFA:

VFA=100\,\dfrac{VMA-V_a}{VMA}=100\,\dfrac{14.27-3.71}{14.27}=74.0\%

\boxed{V_a=3.71\%,\ VMA=14.3\%,\ VFA=74.0\%}

. Sanity check:

V_a=3.71\%

is just below the

4.0\%

design target, so the optimum binder content is slightly LESS than

5.0\%

(less binder raises voids toward

4\%

). VMA exceeds the common

13\%

minimum and VFA sits inside the typical

65

–

78\%

band — internally consistent.

V_a=100\!\left(1-\dfrac{2.441}{2.535}\right)=3.71\%,\quad VFA=100\,\dfrac{14.27-3.71}{14.27}=74.0\%

Effect of adding water on strength

Problem. A mix has $564\ \text{lb}$ of cement and $254\ \text{lb}$ of water per cubic yard. To boost slump, a crew adds $30\ \text{lb}$ of water per cubic yard without changing cement. By how much does the water-cement ratio change, and qualitatively what happens to strength?

Solution. Original

w/c=254/564=0.450

. New water

=254+30=284\ \text{lb}

, so new

w/c=284/564=0.504

. Change

=\dfrac{30}{564}=0.053

(exactly

0.50354-0.45035

), a

12\%

increase in

w/c

\boxed{w/c \text{ rises } 0.45\to0.50}

, an increase of about

0.053

. Sanity check: by Abrams' law strength varies inversely with

B^{w/c}

, so raising

w/c

0.05

drops

28

-day strength on the order of

700

–

1000\ \text{psi}

for a typical mix — confirming the field maxim that adding water to chase slump quietly trades away strength. The fix is a superplasticizer, not water.

\Delta(w/c)=\dfrac{284}{564}-\dfrac{254}{564}=\dfrac{30}{564}=0.053

Common pitfalls

•Mixing mass and volume proportions. The water-cement ratio is a MASS ratio; the batch balance is a VOLUME balance. Convert every mass to absolute volume with $V=W/(SG\,\gamma_w)$ before summing.
•Omitting air from the volume balance. Entrained/entrapped air occupies real volume ( $5\%$ of $27\ \text{ft}^3=1.35\ \text{ft}^3$ ); leaving it out oversizes the aggregate and fails to close at $27\ \text{ft}^3$ .
•Using $\gamma_w$ wrong: $62.4\ \text{lb/ft}^3$ in USCS, $1000\ \text{kg/m}^3$ (or $9.81\ \text{kN/m}^3$ ) in SI. A density-vs-specific-weight slip throws every absolute volume off.
•Computing VMA with $G_{mm}$ instead of the aggregate bulk specific gravity $G_{sb}$ . VMA is about aggregate packing — it must use $G_{sb}$ ; using $G_{mm}$ or $G_{se}$ gives a wrong, usually too-low, VMA.
•Forgetting $P_s=1-P_b$ in VMA, or mixing percent and decimal forms. If $P_b=5.0\%$ then $P_s=0.95$ (or $95\%$ ) — be consistent with $G_{mb}$ and $G_{sb}$ .
•Reading optimum binder content from peak stability alone. Superpave sets optimum at $4.0\%$ air voids; the binder content that maximizes Marshall stability is generally drier than the volumetric optimum.
•Adding water to increase slump. It works but raises $w/c$ and cuts strength and durability; the proper workability tool is a water reducer/superplasticizer at constant $w/c$ .

References

NCEES FE Reference Handbook — Materials Science/Structure of Matter: Concrete — Source of the strength-vs-water/cement relationship, air entrainment for durability, and workability notes.
ACI 211.1 — Standard Practice for Selecting Proportions for Normal, Heavyweight, and Mass Concrete — The absolute-volume proportioning procedure.
Asphalt Institute MS-2 — Asphalt Mix Design Methods — Superpave and Marshall volumetric definitions: $V_a$ , VMA, VFA, and optimum binder content at 4% air voids.
AASHTO M 323 / R 35 — Superpave Volumetric Mix Design — Design criteria for air voids, VMA, and VFA by nominal maximum aggregate size and traffic level.

B. Test methods and specifications

Test Methods and Specifications

The standardized tests that turn materials into accepted work — concrete cylinders and slump, steel tension, aggregate gradation and specific gravity, asphalt content, and wood grading.

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C. Physical and mechanical properties

Physical and Mechanical Properties of Civil Materials

Stiffness, strength, and ductility of steel, concrete, aggregate, asphalt, and wood — the elastic constants and stress-strain landmarks that every structural and materials calculation rests on.

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