Testing, mix design, and durability

This chapter covers the following:

• Concrete strength testing requirements and sampling criteria
• Definition and evaluation of compressive strength tests
• Acceptable strength criteria and structural adequacy requirements
• Field-cured cylinders and core testing standards
• Concrete mix design parameters, including yield and absolute volume
• Water-cement ratio and cementitious material components
• Aggregate moisture conditions and calculations
• Aggregate properties, including density, absorption, and specific gravity
• Concrete maturity and time-temperature relationships
• Concrete exposure categories and classification systems

FE tip: The acceptance criteria, yield, absolute volume, and water-cement ratio equations in this chapter are printed in the FE Reference Handbook’s concrete materials section - practice locating them there rather than memorizing every form.

Concrete strength testing requirements

Sampling frequency

• Samples for strength tests of each class of concrete placed each day shall be taken not less than:
  • Once per day, and
  • Once for each $150y{d}^3$ of concrete, or
  • Once for each $5000f{t}^2$ of slab or wall surface area (whichever governs).

Small quantities

• When total quantity of a given class of concrete is less than 50 yd³:
  • Strength tests are not required if evidence of satisfactory strength is submitted and approved by the building official.

Strength test definition

• A strength test is the average compressive strength of:
  • At least two 6 in. × 12 in. cylinders, or
  • At least three 4 in. × 8 in. cylinders
• Cylinders are made from the same sample and tested at 28 days, or at the designated test age.

Specified strength notation

• Let:

$$f_c^{\prime }=\text{Specified compressive strength of concrete (psi)}$$

Acceptable strength criteria

The strength level of an individual concrete class is satisfactory if:

1. Three-test average requirement:

$$\text{Every arithmetic average of any three consecutive strength tests}\ge f_c^{\prime }$$

2. No single test underperformance:

   • If:

$$f_c^{\prime }\le 5000psi\Rightarrow \text{No test}<f_c^{\prime }-500\text{psi}$$

• If:

$$f_c^{\prime }>5000psi\Rightarrow \text{No test}<0.90\cdot f_c^{\prime }$$

Field-cured cylinders

• If field-cured cylinder strength at test age is less than 85% of that of companion lab-cured cylinders, the procedures for protecting and curing the in-place concrete must be improved.

• Exception: This 85% limit does not apply if field-cured strength exceeds:

$$f_c^{\prime }+500\text{psi}$$

Core tests for existing structures

• Concrete cores from structures must be tested no earlier than 48 hours nor later than 7 days after coring, and at least 5 days after last being wetted (unless otherwise approved by the building official), per ACI 318 / ASTM C42.

Structural adequacy criteria

Let the average of 3 core strengths be denoted as ${\bar{f}}_{core}$.

Concrete is structurally adequate if:

1. Average strength:

$${\bar{f}}_{core}\ge 0.85\cdot f_c^{\prime }$$

2. Minimum single core strength:

$$f_{core,\text{min}}\ge 0.75\cdot f_c^{\prime }$$

Concrete mix design parameters

Yield

Yield is the volume of fresh concrete produced from a batch:

$$\text{Yield}=\frac{\text{Total mass of batched materials}}{\text{Density of freshly mixed concrete}}=\sum \text{(Absolute volumes of concrete ingredients)}$$

Absolute volume

The absolute volume of a concrete ingredient is calculated as:

$$\text{Absolute volume}=\frac{\text{Mass of loose material}}{\text{Relative density (or specific gravity)}\times \text{Density of water}}$$

Example: Absolute volume and yield

A batch contains 500 lb of cement ($G=3.15$), 235 lb of water ($G=1.00$), 1200 lb of SSD fine aggregate ($G=2.64$), and 1800 lb of SSD coarse aggregate ($G=2.65$). Using ${\rho }_{water}=62.4lb/f{t}^3$, find the yield.

• Cement: $500/(3.15\times 62.4)=2.54f{t}^3$
• Water: $235/(1.00\times 62.4)=3.77f{t}^3$
• Fine aggregate: $1200/(2.64\times 62.4)=7.28f{t}^3$
• Coarse aggregate: $1800/(2.65\times 62.4)=10.89f{t}^3$

Answer: yield $=2.54+3.77+7.28+10.89=24.48f{t}^3$ (about $0.91y{d}^3$)

Aggregate moisture conditions

Relative densities of aggregates are taken under saturated surface-dry (SSD) conditions.

1. Total moisture (%)

$$\text{Total moisture (\%)}=100\times \frac{\text{Wet weight}-\text{Oven-dry weight}}{\text{Oven-dry weight}}$$

2. Absorbed moisture (%) (also called the aggregate’s absorption)

$$\text{Absorbed moisture (\%)}=100\times \frac{\text{SSD weight}-\text{Oven-dry weight}}{\text{Oven-dry weight}}$$

3. Free moisture (%)

$$\text{Free moisture (\%)}=\text{Total moisture (\%)}-\text{Absorbed moisture (\%)}$$

Example: Aggregate moisture content

A fine aggregate sample has a wet mass of 1050 g, an oven-dry mass of 1000 g, and an SSD mass of 1020 g. Find the total, absorbed, and free moisture.

• Total moisture: $100\times (1050-1000)/1000=5.0\%$
• Absorbed moisture: $100\times (1020-1000)/1000=2.0\%$
• Free moisture: $5.0\%-2.0\%=3.0\%$

Answer: the aggregate carries $3.0\%$ more water than SSD requires, so that amount must be subtracted from the batch water.

Watch out: Confirm whether a given aggregate mass or specific gravity is on an oven-dry or SSD basis before using it in an absolute-volume or yield calculation - mixing bases is a common source of error.

Water-cement ratio

The water-cementitious material ratio (w/c) is defined as:

$$w/c=\frac{\text{Mass of water}}{\text{Mass of cementitious materials}}$$

Cementitious materials may include:

• Portland cement
• Blended cement
• Fly ash
• Slag cement
• Silica fume
• Natural pozzolans

Example: Water-cementitious materials ratio

A mix uses 235 lb of water and 517 lb of total cementitious material per cubic yard. Find $w/c$.

Answer: $w/c=235/517=0.45$

Aggregate properties in concrete mix design

Mix designs use the SSD condition as the reference point, since that’s what separates water absorbed inside the aggregate (which doesn’t change the amount of mixing water needed) from water sitting on its surface (which does). The properties below build on that same reference condition, and on the total, absorbed, and free moisture percentages defined above.

SSD (saturated-surface-dry)

• The condition in which the permeable pores of aggregate particles are filled with water as if submerged, but without any free water on the surface of the particles.

Density and specific gravity

The density measures below differ in two ways: which mass they use (oven-dry or SSD) and which volume they use. None of them include the voids between particles. The key distinction to keep straight is which pores count as part of the particle’s volume: oven-dry and SSD density count all pores, permeable and impermeable, while apparent density counts only the impermeable ones.

Bulk specific gravity

Both bulk specific gravity bases below use the same denominator: the mass of water equal to $V_{\text{SSD}}$, the aggregate particle volume including all permeable and impermeable pores. The two bases differ only in which mass goes in the numerator.

Oven-dry basis:

$$G_{\text{bulk, OD}}=\frac{M_{\text{OD}}}{V_{\text{SSD}}\cdot {\rho }_{\text{water}}}$$

SSD basis:

$$G_{\text{bulk, SSD}}=\frac{M_{\text{SSD}}}{V_{\text{SSD}}\cdot {\rho }_{\text{water}}}$$

• Typical range for normal-weight aggregates:

$$G_{\text{bulk, SSD}}=2.4\text{ to }2.9$$

Concrete maturity

Concrete maturity can be estimated using the Time-Temperature Factor method:

$$M=\sum _0^t(T-T_0)\Delta t$$

where

• $M$ = maturity index ($°F$-hours)
• $T$ = average concrete temperature ($°F$) during time interval $\Delta t$
• $T_0$ = datum temperature ($°F$), usually $32°F$ unless otherwise specified
• $t$ = elapsed time ($hr$)
• $\Delta t$ = time intervals ($hr$)

Example: Maturity index

Concrete cures at $70°F$ for 6 hours, then $60°F$ for 4 hours. Using a datum temperature of $32°F$, find the maturity index.

• $(70-32)\times 6=228$
• $(60-32)\times 4=112$

Answer: $M=228+112=340°F\text{-hr}$

Concrete exposure categories and classes

Freezing and thawing (F)

Class	Condition
F0	Concrete not exposed to freezing-and-thawing cycles
F1	Concrete exposed to freezing-and-thawing cycles with limited exposure to water
F2	Concrete exposed to freezing-and-thawing cycles with frequent exposure to water
F3	Concrete exposed to freezing-and-thawing cycles with frequent exposure to water and exposure to deicing chemicals

Other exposure categories

ACI 318 defines three more exposure categories using the same tiered structure as the F-classes above:

• Sulfate (S0-S3): based on water-soluble sulfate in soil or dissolved sulfate in water, ranging from negligible exposure (S0) to severe exposure (S3, above 2.00% in soil or 10,000 ppm in water).
• In contact with water (W0-W2): from concrete kept dry in service (W0), to concrete in contact with water where low permeability isn’t required (W1), to concrete in contact with water where low permeability is required (W2).
• Corrosion protection of reinforcement (C0-C2): from concrete dry or protected from moisture (C0), to concrete exposed to moisture without an external chloride source (C1), to concrete exposed to moisture and an external chloride source such as deicing chemicals or seawater (C2).

For example, a bridge pier exposed to seawater spray falls under C2 (moisture plus an external chloride source), while an interior column protected from moisture falls under C0.

The FE exam more often tests recognizing which category and class a scenario falls into than exact threshold values, so focus on the F-class table above as the model for how each category’s classes are structured.