CELE Geotechnical Engineering — CompactionRevision Notes
Revision notes for CELE Geotechnical Engineering — Compaction. Short, focused, and designed for the week before exam day. Use these when you are already familiar with the chapter and need a quick refresh on the high-yield items Professional Regulation Commission (PRC) — Board of Civil Engineering tests.
Exam context
The Civil Engineer Licensure Examination is conducted by Professional Regulation Commission (PRC) — Board of Civil Engineering and is scheduled for May and November 2026. The Geotechnical Engineering subtest is marked as "Core" in the official pattern, and Compaction appears in position 5th of 11 in the CELE Geotechnical Engineering review rotation. Passing mark: 70% weighted average, no sub-test below 50%. Recent CELE 2026 papers have drawn roughly a meaningful share of questions from this subject.
Compaction - Revision Notes
Compaction is the process of mechanically densifying soil by expelling air from the void spaces, thereby increasing the dry unit weight without significantly changing the water content. It is a fundamental topic in geotechnical engineering and a consistent fixture in the PRC Civil Engineer Licensure Examination. Reviewees must master the Proctor compaction test (both Standard and Modified), the computation of dry unit weight, relative compaction, and the zero-air-voids (ZAV) line. Understanding these concepts is essential for evaluating earthwork specifications — such as those required under DPWH guidelines for road subgrades and embankments — and for interpreting field compaction control data. This chapter consolidates all exam-critical formulas, definitions, worked examples, and common pitfalls in a single efficient review.
Sections
Formulas
Example
γ_moist = 19.5 kN/m³, w = 12% → γ_dry = 19.5 / 1.12 = 17.41 kN/m³
Formula
γ_dry = γ_moist / (1 + w)
Variables
γ_dry = dry unit weight (kN/m³); γ_moist = moist (bulk) unit weight (kN/m³); w = water content expressed as a decimal (e.g., 12% → 0.12)
Application
Convert a field or lab moist unit weight to dry unit weight. This is the single most frequently tested compaction formula on the board exam.
Exam Tips
- Always convert w to decimal before substituting into any phase relationship formula.
- If given γ_dry and w, you can find γ_moist = γ_dry × (1 + w) — know the formula both ways.
- Board problems often embed the conversion γ_dry = γ_moist / (1+w) inside a larger RC or ZAV problem — solve it first before attempting the next step.
- Sketch the compaction curve mentally: dry side is to the left of OMC, wet side is to the right.
Key Points
- Compaction densifies soil by mechanical energy (rollers, rammers, vibrators), reducing air voids without removing pore water.
- The result is an increase in dry unit weight (γ_dry), which improves shear strength, reduces compressibility, and lowers permeability.
- Compaction does NOT squeeze out water; it squeezes out AIR — this is the critical conceptual distinction.
- The compaction curve (γ_dry vs. w) is bell-shaped, peaking at the optimum moisture content (OMC) with the maximum dry unit weight (γ_d,max).
- On the dry side of optimum, soil is stiff and flocculated; on the wet side, soil is soft and dispersed.
- The compaction curve always lies below and to the left of the zero-air-voids line.
- Types of compaction equipment: smooth-drum rollers (granular), sheepsfoot rollers (cohesive clays), pneumatic-tired rollers (general), vibratory rollers (granular — most efficient).
Definitions
Term
Compaction
Definition
The densification of soil by mechanical energy that expels air from the voids, increasing dry unit weight at a given water content.
Importance
Core definition — distinguishes compaction from consolidation (which expels water under sustained load).
Term
Optimum Moisture Content (OMC)
Definition
The water content at which a given compaction energy produces the maximum dry unit weight.
Importance
Target water content for field compaction control; field moisture must be near OMC for efficient compaction.
Term
Maximum Dry Unit Weight (γ_d,max)
Definition
The peak dry unit weight achieved on the compaction curve at the OMC for a specific compaction energy.
Importance
The reference value used to compute relative compaction (RC) for field acceptance testing.
Term
Compaction Curve
Definition
A plot of dry unit weight (y-axis) versus water content (x-axis) obtained from a series of Proctor test points; bell-shaped.
Importance
Visual tool for identifying OMC and γ_d,max; the curve's position shifts with compaction energy.
Section Title
Fundamentals of Soil Compaction
Common Mistakes
- Confusing compaction (expels air) with consolidation (expels water) — a classic board exam trap.
- Using w as a percentage (e.g., 12) instead of a decimal (0.12) in the formula γ_dry = γ_moist / (1 + w).
- Thinking that adding more water always increases density — past the OMC, γ_dry decreases.
- Forgetting that the compaction curve shifts: higher energy → higher γ_d,max AND lower OMC.
Formulas
Example
Standard: E = (0.0245 kN × 0.305 m × 25 × 3) / 9.44×10⁻⁴ m³ ≈ 593 kN·m/m³
Formula
E = (W_hammer × H_drop × N_blows × N_layers) / V_mold
Variables
E = compaction energy per unit volume (kN·m/m³); W_hammer = hammer weight (kN); H_drop = drop height (m); N_blows = blows per layer; N_layers = number of layers; V_mold = mold volume (m³)
Application
Compare compaction energies between Standard and Modified Proctor; occasionally tested directly on board exams.
Exam Tips
- A quick mnemonic: Modified = More energy = More density (higher γ_d,max) = Moisture decreases (lower OMC).
- Board problems may give you the compaction curve data points and ask you to identify γ_d,max — always compute γ_dry for each point first, then pick the maximum.
- The question 'Why does modified Proctor give lower OMC?' answer: higher energy lubricates particle arrangement at lower water content, so less water is needed to achieve optimum densification.
Key Points
- The Proctor test is the standard laboratory method for determining the compaction characteristics of a soil (OMC and γ_d,max).
- Standard Proctor (ASTM D698 / AASHTO T99): 24.5 N hammer, 305 mm drop, 3 layers, 25 blows/layer, 944 cm³ mold.
- Modified Proctor (ASTM D1557 / AASHTO T180): 44.5 N hammer, 457 mm drop, 5 layers, 25 blows/layer, 944 cm³ mold — approximately 4.5× the energy of Standard.
- Modified Proctor energy ≈ 2,700 kN·m/m³ vs Standard ≈ 600 kN·m/m³.
- Effect of increasing compaction energy: γ_d,max INCREASES, OMC DECREASES, and the curve shifts upward and to the left.
- Procedure: compact soil at 5–6 different water contents, measure moist unit weight for each, compute γ_dry, plot and identify peak.
- The compaction curve is parabolic — one peak, symmetric only approximately.
Definitions
Term
Standard Proctor Test
Definition
ASTM D698 compaction test using a 24.5 N rammer dropped 305 mm over 3 layers with 25 blows per layer; produces a lower γ_d,max and higher OMC.
Importance
Baseline reference energy; still used for some highway subgrade specifications in older DPWH standards.
Term
Modified Proctor Test
Definition
ASTM D1557 compaction test using a 44.5 N rammer dropped 457 mm over 5 layers with 25 blows per layer; models heavier modern construction equipment.
Importance
Current industry standard for most earthwork specifications; RC is measured against Modified Proctor γ_d,max in DPWH and most Philippine projects.
Section Title
The Proctor Compaction Test
Common Mistakes
- Swapping Standard and Modified Proctor parameters — memorize: Modified has MORE layers (5 vs 3), HEAVIER hammer (44.5 N vs 24.5 N), and HIGHER drop (457 mm vs 305 mm).
- Stating that Modified Proctor gives a higher OMC — it gives a LOWER OMC and HIGHER γ_d,max.
- Forgetting that the Proctor test is a LABORATORY test — field dry density is compared to it, not the other way around.
Formulas
Example
γ_d,field = 17.41 kN/m³, γ_d,max = 18.5 kN/m³ → RC = (17.41/18.5) × 100% = 94.1% (meets 90%, does not meet 95%)
Formula
RC = (γ_d,field / γ_d,max) × 100%
Variables
RC = relative compaction (%); γ_d,field = field dry unit weight (kN/m³); γ_d,max = laboratory maximum dry unit weight from Modified Proctor (kN/m³)
Application
Field quality control — determine whether a compacted layer meets specification before the next lift is placed.
Example
RC = 95%, γ_d,max = 18.5 kN/m³ → γ_d,field,min = 0.95 × 18.5 = 17.575 kN/m³
Formula
γ_d,field = RC × γ_d,max
Variables
Rearranged form — find the required field dry unit weight given a target RC and known γ_d,max.
Application
Determine the minimum acceptable field dry unit weight before testing begins.
Exam Tips
- A two-step board problem: Step 1 — compute γ_d,field from γ_moist and w; Step 2 — compute RC. Always do Step 1 first.
- If RC < specification, a follow-up question often asks: 'How many additional compaction passes?' — this requires judgment beyond the formula.
- RC = 100% means the field has achieved the lab maximum — practically, RC > 100% is impossible unless field conditions are better than lab (rarely occurs; recheck your numbers if this happens).
Key Points
- Relative Compaction (RC) is the ratio of the field dry unit weight to the laboratory maximum dry unit weight, expressed as a percentage.
- RC is the primary field acceptance criterion for compacted fills, embankments, and subgrades.
- Philippine practice (DPWH Standard Specifications): RC ≥ 95% of Modified Proctor for subgrades and base courses; RC ≥ 90% for general embankment fills.
- RC is used for cohesive and well-graded soils; for clean granular soils, relative density D_r is the preferred index.
- If field γ_dry < target RC × γ_d,max, additional compaction passes are required.
- Field measurement of γ_dry: sand cone test, rubber balloon test, or nuclear density gauge (most common in practice).
Definitions
Term
Relative Compaction (RC)
Definition
The ratio of the field dry unit weight to the maximum dry unit weight from the Proctor test, expressed as a percentage.
Importance
Standard field acceptance criterion for earthworks; must meet project specifications before proceeding to next lift.
Term
Relative Density (D_r)
Definition
Index of compactness for granular soils: D_r = (e_max − e) / (e_max − e_min) × 100%, where e is field void ratio.
Importance
Preferred compaction index for clean sands and gravels where the Proctor test is not applicable.
Section Title
Relative Compaction
Common Mistakes
- Using Standard Proctor γ_d,max instead of Modified Proctor as the denominator — always confirm which test was used.
- Rounding γ_dry too early, leading to an incorrect RC — carry at least 3 significant figures through intermediate calculations.
- Confusing RC (ratio of unit weights) with relative density D_r (ratio involving void ratios) — they apply to different soil types.
Formulas
Example
G_s = 2.68, w = 15% → γ_zav = (2.68 × 9.81) / (1 + 0.15 × 2.68) = 26.29 / 1.402 = 18.75 kN/m³
Formula
γ_zav = (G_s × γ_w) / (1 + w × G_s)
Variables
γ_zav = zero-air-voids dry unit weight (kN/m³); G_s = specific gravity of soil solids (dimensionless, typically 2.60–2.75); γ_w = unit weight of water = 9.81 kN/m³; w = water content as decimal
Application
Plot the ZAV line on the compaction curve graph as the upper boundary; verify that computed γ_dry values are below it.
Exam Tips
- To generate multiple ZAV line points for a graph, compute γ_zav at w = 10%, 15%, 20%, 25% using the same G_s.
- A board question may ask: 'Is the following data point valid?' — check if γ_dry < γ_zav at that w; if not, the data is erroneous.
- The ZAV formula is derived from S = 1 (fully saturated): S × e = w × G_s, e = w × G_s when S=1; substitute into γ_dry = G_s·γ_w/(1+e) to get γ_zav.
Key Points
- The ZAV line represents the theoretical maximum dry unit weight at a given water content when the degree of saturation S = 100% (all voids filled with water, zero air).
- The ZAV line is not achievable in practice — real compacted soil always retains some air.
- The compaction curve ALWAYS lies BELOW and to the LEFT of the ZAV line — this is a fundamental geometric constraint.
- The ZAV line is plotted on the same axes as the compaction curve to provide an upper bound reference.
- A family of ZAV lines can be drawn for different G_s values; higher G_s shifts the ZAV line upward.
- The gap between the ZAV line and the compaction curve represents the air voids content in the compacted soil.
Definitions
Term
Zero-Air-Voids (ZAV) Line
Definition
The locus of dry unit weight values corresponding to a degree of saturation S = 100% for varying water contents — the theoretical maximum achievable by compaction.
Importance
Provides the upper bound for the compaction curve; any computed γ_dry exceeding γ_zav at the same w is physically impossible and indicates an error.
Term
Air-Voids Content
Definition
The volume of air expressed as a fraction or percentage of total soil volume: A_v = V_air / V_total = (γ_zav − γ_dry) / γ_w (approximate).
Importance
Quantifies how close the compacted soil is to full saturation; smaller A_v means denser, more effectively compacted soil.
Section Title
Zero-Air-Voids (ZAV) Line
Common Mistakes
- Placing the ZAV line BELOW the compaction curve — it must always be ABOVE.
- Using w as a percentage (not decimal) in the ZAV formula — gives a wildly incorrect answer.
- Forgetting to use γ_w = 9.81 kN/m³ (some reviewees mistakenly use 10 kN/m³ — only acceptable if the problem explicitly states so).
- Assuming G_s = 2.65 for all soils — always use the value given in the problem.
Formulas
Example
G_s = 2.70, e = 0.60 → γ_dry = 2.70×9.81/1.60 = 16.54 kN/m³
Formula
γ_dry = G_s · γ_w / (1 + e)
Variables
G_s = specific gravity; γ_w = 9.81 kN/m³; e = void ratio
Application
Find γ_dry when void ratio is known, or back-calculate e from a known γ_dry.
Example
S=0.80, e=0.50, G_s=2.70 → w = S·e/G_s = 0.80×0.50/2.70 = 0.148 = 14.8%
Formula
S · e = w · G_s
Variables
S = degree of saturation (decimal); e = void ratio; w = water content (decimal); G_s = specific gravity
Application
Find any one of S, e, w, G_s given the other three; specifically, at S=1 it yields the ZAV condition.
Exam Tips
- Draw a three-phase diagram (solids, water, air) for any unfamiliar compaction problem — it organizes the unknowns systematically.
- The relation S·e = w·G_s is the most powerful single equation in phase relationships — memorize it cold.
Key Points
- Compaction problems are embedded within the broader framework of soil phase relationships — mastery of these is prerequisite.
- Void ratio e and porosity n: e = n/(1−n); n = e/(1+e).
- Degree of saturation S: S·e = w·G_s (this relation generates the ZAV formula when S=1).
- Moist unit weight: γ = G_s·γ_w·(1 + w)/(1 + e).
- Dry unit weight: γ_dry = G_s·γ_w/(1 + e) = γ_moist/(1 + w).
- These relationships allow you to move between γ_dry, e, w, G_s, and S in multi-step board problems.
Definitions
Term
Void Ratio (e)
Definition
Volume of voids divided by volume of solids: e = V_v / V_s.
Importance
A decrease in e during compaction directly corresponds to the increase in γ_dry; tracking e is the most precise way to describe densification.
Term
Degree of Saturation (S)
Definition
Ratio of volume of water to volume of voids: S = V_w / V_v; ranges from 0 (dry) to 1 (saturated).
Importance
At S=1, the ZAV condition is reached; compacted soils on the wet side of optimum approach S ≈ 0.85–0.95.
Section Title
Phase Relationships and Supporting Formulas
Common Mistakes
- Mixing up void ratio e (voids/solids) with porosity n (voids/total) — board problems can test either.
- Forgetting that when S=1 in S·e = w·G_s, you get e = w·G_s, which is the foundation of the ZAV formula.
Connections
- Soil Phase Relationships: All compaction formulas (γ_dry, γ_zav, RC) are derived from the three-phase diagram — mastery of phase relationships is the prerequisite for compaction calculations.
- Shear Strength: Compaction increases effective stress and reduces void ratio, directly improving friction angle and cohesion — connects to bearing capacity and slope stability.
- Consolidation vs Compaction: Consolidation (Chapter on Settlement) expels water from saturated clays under sustained load; compaction expels air from unsaturated soils by mechanical energy — opposite mechanisms, both increase γ_dry.
- Permeability: Compaction reduces void ratio and creates a more tortuous flow path, lowering hydraulic conductivity — essential for dam cores and liner systems (geoenvironmental).
- Earthwork and Embankment Design: RC specifications directly govern DPWH highway embankment and subgrade construction — connects to pavement design and foundation engineering.
- Relative Density vs Relative Compaction: D_r (granular soils) and RC (cohesive/general fills) are parallel concepts for field compaction control — know when to apply each.
- Field Testing Methods: Sand cone test (ASTM D1556), rubber balloon test (ASTM D2167), and nuclear gauge (ASTM D6938) are the field counterparts to the Proctor test — connects laboratory to field practice.
- Proctor Energy and Compaction Equipment: The energy levels of Standard and Modified Proctor are calibrated to represent light and heavy construction equipment, respectively — connects lab procedure to real construction practice.
Exam Strategy
For PRC board exam problems on compaction, follow a strict three-step protocol: (1) IDENTIFY what is given — moist unit weight, water content, G_s, and any specification (RC requirement). (2) CONVERT — change w from percent to decimal before any formula substitution; identify whether Standard or Modified Proctor is referenced. (3) SOLVE in sequence — always compute γ_dry first from γ_moist and w, then compute RC or γ_zav as required. The most dangerous trap is substituting w as a percentage (e.g., 12 instead of 0.12), which gives an answer an order of magnitude off — immediately flag it by checking whether γ_dry is reasonably less than γ_moist. On the ZAV line, verify your answer passes the sanity check: γ_dry (computed) < γ_zav (at the same w). For multi-step problems, write out the formula, list knowns, substitute, and compute — never skip intermediate steps. Memorize the four key equations cold: γ_dry = γ/(1+w), RC = γ_d,field/γ_d,max, γ_zav = G_s·γ_w/(1+w·G_s), and S·e = w·G_s. These four cover approximately 90% of all board compaction questions. Budget 2–3 minutes per compaction problem; problems with both γ_dry and RC or ZAV take up to 4 minutes — pace accordingly within the time limit.
Quick Review Questions
A compacted soil sample has a moist unit weight of 20.2 kN/m³ at a water content of 14%. Compute the dry unit weight.
Apply γ_dry = γ_moist / (1 + w). Convert w = 14% to 0.14. Divide 20.2 by 1.14 to get 17.72 kN/m³. This is the most fundamental compaction computation.
The laboratory maximum dry unit weight from a Modified Proctor test is 18.9 kN/m³. A field test yields γ_dry = 17.8 kN/m³. Compute the relative compaction and determine if it meets a 95% specification.
RC = (γ_d,field / γ_d,max) × 100% = (17.8/18.9) × 100% = 94.18%. Since 94.2% < 95%, the layer fails the acceptance criterion and requires additional compaction passes.
Compute the zero-air-voids dry unit weight for G_s = 2.70 at water content w = 10%.
Substitute G_s = 2.70, γ_w = 9.81 kN/m³, and w = 0.10 into γ_zav = G_s·γ_w / (1 + w·G_s). Numerator = 26.487; denominator = 1.27; result = 20.86 kN/m³. Any actual γ_dry at w=10% must be below this value.
Compute the zero-air-voids dry unit weight for G_s = 2.70 at water content w = 20%.
Same formula with w = 0.20. Denominator = 1 + 0.54 = 1.54. Result = 26.487/1.54 = 17.20 kN/m³. Notice the ZAV unit weight decreases as w increases — the ZAV line slopes downward to the right.
Why does the Modified Proctor test yield a lower OMC than the Standard Proctor test for the same soil?
With greater energy input, the soil can be compacted to a higher γ_dry with less water. The lubrication effect of water becomes effective at a lower w when more mechanical energy is available, shifting the OMC to the left and γ_d,max upward on the compaction curve.
A project requires RC ≥ 95% of Modified Proctor. If γ_d,max = 18.5 kN/m³, what is the minimum acceptable field dry unit weight?
Rearrange RC = γ_d,field / γ_d,max to get γ_d,field = RC × γ_d,max = 0.95 × 18.5 = 17.575 kN/m³. Any field measurement below this value means the layer is under-compacted.
A computed point on the compaction curve gives γ_dry = 19.1 kN/m³ at w = 15%, but the zero-air-voids γ_dry at the same water content is 18.75 kN/m³. What does this indicate?
The compaction curve can NEVER exceed the ZAV line because that would imply negative air volume (impossible). If γ_dry > γ_zav at the same w, recheck mass measurements, volume of mold, or water content determination for computational or experimental errors.
For a compacted soil with G_s = 2.68, S = 0.85, and e = 0.45, what is the water content?
Use the fundamental phase relationship S·e = w·G_s, rearranged as w = S·e / G_s. Substitute and compute. This bridges phase relationships with compaction — a common multi-step board problem type.
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