Compaction - Cheat Sheet
Your last-minute revision companion for Proctor testing, relative compaction, and zero-air-voids concepts. Master the formulas and board-exam pitfalls in 30 minutes.
Proctor Test & Maximum Dry Unit Weight
Formulas
γ_dry = γ / (1 + w)
Meaning
γ_dry = dry unit weight (kN/m³), γ = moist unit weight (kN/m³), w = water content (decimal, not %)
Watch out
w must be in DECIMAL form (12% = 0.12). Using w as percentage (12) will give wrong answer by ~10× or more. Always divide moist by (1 + w), not (1 + w%).
When to use
Convert moist field or lab measurement to dry unit weight for compaction analysis
γ_d,max (Standard) < γ_d,max (Modified)
Meaning
Maximum dry density; Modified Proctor yields higher density than Standard due to greater compaction energy
Watch out
Modified Proctor ALSO has LOWER OMC (optimum moisture) than Standard. Don't assume same OMC with higher energy.
When to use
Comparing lab results or spec requirements — identify which Proctor method applies
Common values
Value
2.49 kg
Symbol
m_std
Quantity
Standard Proctor hammer mass
Value
4.54 kg
Symbol
m_mod
Quantity
Modified Proctor hammer mass
Value
0.305 m (12 in)
Symbol
h_std
Quantity
Standard Proctor drop height
Value
0.457 m (18 in)
Symbol
h_mod
Quantity
Modified Proctor drop height
Value
12–20%
Symbol
OMC
Quantity
Typical fine-grained soil OMC range
Value
6–12%
Symbol
OMC
Quantity
Typical sandy soil OMC range
Important facts
- DRY side of OMC (w < OMC): γ_dry increases with w as air is expelled. More water = more pore-fluid pressure aids compaction.
- WET side of OMC (w > OMC): γ_dry decreases with w as water replaces solid particles. Excess water prevents further densification.
- Compaction curve ALWAYS lies BELOW zero-air-voids line (soil always retains some air).
- Modified Proctor: ~10–15% higher γ_d,max and 2–5% lower OMC compared to Standard for typical cohesive soils.
- Moist unit weight γ = (solids + water) / volume; dry unit weight γ_dry = solids only / volume.
Key definitions
Optimum Moisture Content (OMC)
Example
Typical fine-grained soil: OMC ≈ 12–18%; Modified Proctor OMC < Standard OMC for same soil.
Water content at which soil achieves maximum dry unit weight during Proctor compaction.
Standard Proctor
Example
Used for preliminary design; common in older Philippine road standards.
Compaction test using 24.5 kN hammer, 0.305 m drop, 3 layers, 25 blows/layer; produces lower γ_d,max.
Modified Proctor
Example
Typical current Philippine standard for fills, subgrades; more stringent field control.
Higher-energy compaction: 44.5 kN hammer, 0.457 m drop, 5 layers, 25 blows/layer; higher γ_d,max.
Compaction Curve
Example
Dry side: w < OMC, fewer air voids expelled, lower γ_dry. Wet side: w > OMC, water replaces solids, γ_dry decreases.
Plot of γ_dry (y-axis) vs w (x-axis) from Proctor test; peak = γ_d,max at OMC.
Diagrams to know
- Proctor curve: bell-shaped γ_dry vs w plot with OMC marked at peak.
- Moist vs Dry unit weight: show γ = γ_dry(1+w) relationship as a line through origin.
- Standard vs Modified: overlay two curves showing Modified higher and leftward-shifted.
Relative Compaction (RC) & Field Control
Formulas
RC = (γ_d,field / γ_d,max) × 100%
Meaning
RC = relative compaction (%), γ_d,field = field dry unit weight (kN/m³), γ_d,max = lab maximum (kN/m³)
Watch out
MUST use γ_d values (dry), not moist γ. Common error: using γ_moist gives inflated RC (can exceed 100% falsely). Always convert field sample to γ_d first.
When to use
Compare achieved field compaction to lab standard; used for quality control on fills, subgrades, pavements.
Common values
Value
90–95%
Symbol
RC_min
Quantity
Minimum RC for subgrades (Philippine roads)
Value
17.0–18.5 kN/m³
Symbol
γ_d,field
Quantity
Typical field γ_d,field (fine-grained)
Value
17.5–19.0 kN/m³
Symbol
γ_d,max
Quantity
Typical lab γ_d,max (Modified Proctor)
Important facts
- RC > 100% is IMPOSSIBLE with Proctor reference; if calculated, field data or lab test is faulty.
- Field samples: use core drilling (undisturbed) or sand replacement method (sand cone) for γ_d,field measurement.
- Typical field γ_d,field = 17–18.5 kN/m³ for fine-grained soils; modify by soil type and energy applied.
- Seasonal variation: moisture content in field changes; compaction must be verified at multiple locations and depths.
- Fail = RC below spec → rework (re-compact, add moisture control, etc.); retest required.
Key definitions
Relative Compaction (RC)
Example
RC = 94% means field achieved 94% of lab γ_d,max; if spec requires ≥95%, this fails (marginally).
Ratio of field achieved dry unit weight to lab maximum, expressed as percentage; measure of fill compaction quality.
Specification Requirement
Example
Critical structures: RC ≥ 95%; less critical embankments: RC ≥ 90%.
Typical Philippine specs (DPWH, road standards): RC ≥ 90–95% (Modified Proctor) for subgrades, fills.
Diagrams to know
- RC vs depth profile: plot RC as function of fill depth; identify weak zones.
- Pass/fail band: RC range with shaded region for acceptable (≥90–95%) and unacceptable (<90%) zones.
Zero-Air-Voids (ZAV) Line & Air Content
Formulas
γ_zav = (G_s × γ_w) / (1 + w × G_s)
Meaning
γ_zav = zero-air-voids unit weight (kN/m³), G_s = specific gravity of solids (dimensionless), γ_w = unit weight of water (9.81 kN/m³), w = water content (decimal)
Watch out
w must be DECIMAL (0.12, not 12). Numerator (G_s × γ_w) is often 26–27 kN/m³; denominator (1 + w × G_s) grows with w, so γ_zav decreases as w increases (counterintuitive!).
When to use
Draw upper theoretical bound on Proctor curve; verify compaction curve lies below (always some air retained).
Air content n_a = (γ_zav - γ_dry) / γ_w × 100%
Meaning
n_a = percent air voids in compacted soil; difference between ZAV line and actual compaction curve.
Watch out
ZAV curve is asymptotic; as w approaches soil saturation, γ_zav approaches γ_sat. Never expect compaction curve to reach ZAV line in practice.
When to use
Calculate void ratio or air percentage at a given water content; verify compaction effectiveness.
Common values
Value
2.65–2.75
Symbol
G_s
Quantity
Typical G_s for cohesive soils
Value
2.60–2.70
Symbol
G_s
Quantity
Typical G_s for sandy soils
Value
9.81 kN/m³ (or ≈ 10 kN/m³ for approximation)
Symbol
γ_w
Quantity
Unit weight of water
Value
5–10%
Symbol
n_a
Quantity
Typical air content at OMC (compacted)
Important facts
- Compaction curve shape: rises from dry side, peaks at OMC (maximum γ_dry), descends on wet side — ALL curve points are BELOW ZAV.
- As water content increases toward saturation, both γ_dry and γ_zav eventually converge to γ_sat, but compaction tests don't reach that region.
- ZAV equation: numerator (G_s × γ_w) is constant ~26–27 kN/m³; denominator (1 + w × G_s) increases with w, so ZAV curve slopes downward.
- Air content at OMC is typical 5–10% for well-compacted cohesive soils; higher on dry side, lower (approaching zero) as w increases.
- A point ABOVE ZAV line indicates calculation error or faulty lab/field data; recalculate or retest.
Key definitions
Zero-Air-Voids (ZAV) Line
Example
At w = 15%, G_s = 2.68: γ_zav = 18.75 kN/m³; any actual compaction γ_dry ≤ 18.75 kN/m³.
Theoretical locus of γ_dry at 100% saturation (S = 100%, no air) for varying water content; upper bound for compaction curve.
Saturation Line (S = 100%)
Example
Approach but never reach in Standard or Modified Proctor on dry side; fully saturated soil is soft (poor bearing).
Same as ZAV line; all voids filled with water, no air voids present.
Air-Voids Content
Example
S = 70% (saturated) → 30% air voids.
Percentage of volume occupied by air (not water, not solids); complement of saturation degree S.
Diagrams to know
- Proctor curve WITH ZAV line: bell-shaped curve below straight/curved upper bound; show gap = air content.
- ZAV line construction: straight line from intercept at w=0, w=OMC, w=saturation; different shape depending on plot scale.
- Three curves overlay: Standard, Modified, ZAV; Modified higher and leftward.
Reactions or equations
γ_sat = γ_dry + w × G_s × γ_w / (1 + e) [alternate form using void ratio e]
Note
ZAV is a special case of saturation curve; useful for quick graphical check without computing e.
Conditions
At full saturation (S = 100%); requires void ratio e or porosity n.
S = (w × G_s) / e × 100% [saturation degree]
Note
At S = 100%, the equation γ_zav is derived from this; ZAV line is NOT the same as Proctor wet-side curve.
Conditions
For any soil state; e = void ratio.
Compaction Mechanisms & Practical Considerations
Common values
Value
~600 kJ/m³
Symbol
E_std
Quantity
Compaction energy — Standard Proctor
Value
~2700 kJ/m³
Symbol
E_mod
Quantity
Compaction energy — Modified Proctor
Value
1000–2000 kJ/m³ (varies by pass count, soil type)
Symbol
E_field
Quantity
Typical field vibratory roller energy
Important facts
- Compaction EXPELS AIR, not water; adding excess water past OMC forces air out but water (incompressible) replaces solids, lowering γ_dry.
- Dry side (w < OMC): Air expulsion rate > water infiltration; γ_dry increases with w.
- Wet side (w > OMC): Water infiltration rate > air expulsion; γ_dry decreases with w; pore pressure builds, reducing effective stress.
- Field compaction uses vibratory rollers, sheepsfoot rollers (static + kneading), impact rollers; less energy than Modified Proctor typical for fills.
- Cohesive soils (clay, silt) sensitive to OMC; granular soils (sand) less sensitive but still benefit from optimal moisture.
- Specification: Field compaction should match or exceed lab test standard (e.g., Modified Proctor reference for 95% RC target).
Key definitions
Compaction Energy
Example
Modified Proctor: ~2700 kJ/m³; Standard Proctor: ~600 kJ/m³.
Mechanical work applied per unit volume (kJ/m³) to densify soil; determined by hammer mass, drop height, number of layers, and blows.
Static Compaction
Example
Vibratory roller on road subgrade; less reliance on water content control than Proctor method.
Sustained pressure (e.g., vibratory plate, rollers) to densify soil; effective for granular materials.
Dynamic Compaction
Example
Manual rammer, mechanical tamper; Proctor test simulates field dynamic compaction.
Repeated impact (drop hammer, vibratory) to expel air; modeled by Proctor test.
Relative Density (D_r)
Example
NOT used for clays; compaction spec for sand often uses D_r ≥ 75% instead of RC ≥ 95%.
For GRANULAR soils only: D_r = (γ_d,max − γ_d,field) / (γ_d,max − γ_d,min) × 100%; alternative to RC for sands.
Diagrams to know
- Compaction energy effect: overlay curves for Standard, Modified, and higher-energy tests; show rightward shift and upward peak.
- Mechanism sketch: dry side (air expelled, density up) vs wet side (water replaces solids, density down); label pore pressure buildup.
- Field roller types: vibratory (effective on granular), sheepsfoot (kneading action on clay), smooth drum (finish layer).
Philippine Standards & Exam Board References
Common values
Value
90–95%
Symbol
RC_min
Quantity
Typical Philippine fill spec: RC minimum
Value
1V:2H to 1V:3H (soil type, height dependent)
Symbol
Slope
Quantity
Typical embankment slope (after compaction)
Important facts
- Philippine specs often default to Modified Proctor for modern construction (post-2000s) due to higher control and durability.
- Board exams expect clear distinction between Standard and Modified (energy, OMC, γ_d,max).
- RC calculation and interpretation is a MUST-KNOW topic; appears in nearly every geotechnical licensure exam.
- ZAV concept is often tested indirectly (recognizing impossible compaction points, understanding saturation limits).
- Field compaction control: SPT, cone penetration, density in-situ testing; board may ask which method to use for different soil types.
Key definitions
DPWH Standard
Example
Expressway, provincial road subbase: Modified Proctor reference, RC ≥ 95%.
Philippine Department of Public Works and Highways specification for road fills and subgrades; typically requires RC ≥ 95% (Modified Proctor).
NSCP 2015 Geotechnical Provisions
Example
Building foundation fills often require RC ≥ 90% (Modified Proctor); site-specific based on structure importance.
Philippine National Structural Code of the Philippines 2015 Chapter 2 covers soil investigation, compaction specs for foundations and fills.
PRC Licensure Exam Board Focus
Example
Common board question: given lab γ_d,max and field sample (moist weight + water content), calculate RC and pass/fail assessment.
Proctor test (standard vs modified), RC calculation, ZAV concept, and typical compaction failures are high-yield topics.
Diagrams to know
- Philippine compaction spec flowchart: structure type → required RC (≥90% or ≥95%) → select Proctor standard → set field control plan.
- Board exam decision tree: given Proctor data, decide Standard vs Modified, interpret RC result.
Must remember
- FORMULA #1: γ_dry = γ / (1 + w) — water content w MUST be DECIMAL (0.12 not 12), or answer is off by 10× or more.
- FORMULA #2: RC = (γ_d,field / γ_d,max) × 100% — MUST use DRY unit weights; using moist γ yields wrong (inflated) RC.
- PROCTOR HIERARCHY: Modified > Standard in energy, γ_d,max, and OMC (Modified OMC is LOWER). Typical current spec: Modified Proctor, RC ≥ 95%.
- ZAV LINE: Theoretical upper bound; compaction curve ALWAYS below it. If your plotted point exceeds ZAV, RECALCULATE or flag as error.
- DRY vs WET SIDE: Dry side (w < OMC) → γ_dry increases with water (air expelled). Wet side (w > OMC) → γ_dry decreases with water (water replaces solids).
- ZERO-AIR-VOIDS: γ_zav = (G_s × γ_w) / (1 + w × G_s) — w in DECIMAL; as w increases, γ_zav DECREASES (counterintuitive but true).
- RC INTERPRETATION: RC ≥ 95% = excellent; 90–95% = acceptable; < 90% = FAIL (rework required). Know Philippine DPWH / NSCP thresholds.
- RELATIVE DENSITY D_r: For GRANULAR soils only; NOT for clay. D_r = (γ_d,max − γ_d) / (γ_d,max − γ_d,min) × 100%.
- COMMON EXAM TRAP: Calculating RC > 100% indicates ERROR — likely used moist γ instead of dry γ, or wrong reference value.
- BOARD SCENARIO: Given moist sample + water content + lab γ_d,max → calculate dry γ → calculate RC → assess pass/fail. This 3-step flow appears EVERY exam.
Last minute tips
- TIP #1 — Unit Weight Conversion: Always convert moist field sample to γ_dry FIRST before calculating RC. Mistake: skipping this step and using γ_moist directly in RC formula causes 10–15% error and likely exam failure on this problem.
- TIP #2 — ZAV Sanity Check: After plotting or calculating a compaction point, quickly verify it is BELOW the ZAV line. If above, STOP and recheck your G_s, w, and γ_dry values — one is wrong. This is a board-exam red flag.
- TIP #3 — Proctor Energy Ratio: Modified = ~4.5× Standard energy (~2700 kJ/m³ vs ~600 kJ/m³). Remember: higher energy → higher γ_d,max AND LOWER OMC. Many students confuse the OMC trend.
- TIP #4 — RC Threshold Memorization: Philippine standard for modern fills = Modified Proctor, RC ≥ 95%. Embankments may allow 90%. If exam asks 'does this fill pass?', check against 95% first; if below 90%, definitely fails.
- TIP #5 — Read the Question Context: If problem gives Proctor method, water content, and field sample — IT WANTS RC CALCULATION. Set up γ_dry, then RC in two steps. Don't mix in D_r or other concepts unless explicitly asked for granular soil analysis.
Comparison tables
Standard vs Modified Proctor Test
| Parameter | Standard Proctor | Modified Proctor |
|---|---|---|
| Hammer mass | 2.49 kg | 4.54 kg (heavier) |
| Drop height | 0.305 m (12 in) | 0.457 m (18 in) (higher) |
| Number of layers | 3 layers | 5 layers |
| Blows per layer | 25 blows | 25 blows |
| Total compaction energy | ~600 kJ/m³ (LOW) | ~2700 kJ/m³ (HIGH) |
| γ_d,max (result) | LOWER | HIGHER (~10–15% above Standard) |
| OMC (result) | HIGHER | LOWER (~2–5% below Standard) |
| When used | Preliminary design, older specs | Current Philippine construction, critical structures |
| Typical RC spec requirement | ≥ 90% | ≥ 95% |
Relative Compaction (RC) vs Relative Density (D_r)
| Aspect | Relative Compaction (RC) | Relative Density (D_r) |
|---|---|---|
| Formula | RC = (γ_d,field / γ_d,max) × 100% | D_r = (γ_d,max − γ_d,field) / (γ_d,max − γ_d,min) × 100% |
| Used for | Cohesive soils (clay, silt); all soil types in general | GRANULAR soils ONLY (sand, gravel) |
| Reference values needed | γ_d,max (from Proctor test) | γ_d,max AND γ_d,min (loose and dense states) |
| Result interpretation | RC < 90% = poor; RC ≥ 95% = excellent | D_r < 35% = loose; D_r ≥ 75% = dense |
| Proctor test relevance | YES, directly from Proctor γ_d,max | NOT typically used; alternative to Proctor for sands |
Dry Side vs Wet Side of Optimum Moisture Content (OMC)
| Feature | DRY SIDE (w < OMC) | WET SIDE (w > OMC) |
|---|---|---|
| Water content | Below optimum | Above optimum |
| Air expulsion | RATE increases with added water | RATE decreases; water fills voids instead |
| γ_dry trend | INCREASES as w increases | DECREASES as w increases |
| Compaction effectiveness | HIGH; more compaction gain per unit water | LOW; diminishing return; pore pressure buildup |
| Pore water pressure | LOW; partial saturation | INCREASES; reduces effective stress, impedes compaction |
| Field concern | Difficult to compact; may need water addition or re-working | Risk of instability, pumping in pavement; ensure adequate drainage |
Common Compaction Failures & Root Causes
| Failure Symptom | Most Likely Cause | Remedy |
|---|---|---|
| RC < 90% | Insufficient compaction energy; too many passes omitted; poor supervision | Increase passes; verify roller type/settings; retest frequently |
| RC > 100% (impossible value) | ERROR in calculation; used moist γ instead of dry γ; wrong lab reference γ_d,max | RECALCULATE using γ_dry = γ_moist / (1+w). Retest field and lab samples. |
| Compacted point ABOVE ZAV line | Lab data error; field sample contamination or faulty density measurement | Recalculate ZAV. Retest with proper procedure (sand cone, core, nuclear gauge). |
| High variability in RC across fill | Inconsistent compaction (missed zones, varying passes, uneven moisture); poor work plan | Intensive testing grid; enforce uniform process; check baseline soil uniformity |
| Moisture content WAY off spec | No moisture control (rain, evaporation); fill material source mismatch | Cover stockpiles; pre-wet material if dry-side; drain if saturated; proctor retest |
Diagrams
Compaction Concepts & Formulas
Mind map showing the hierarchy of compaction concepts: Proctor test types (Standard vs Modified), dry unit weight formula, relative compaction calculation, zero-air-voids theory, and soil state categories (dry vs wet side of OMC). Central to all compaction board-exam problems.
Compaction Problem-Solving Flowchart for Board Exams
Step-by-step flowchart for solving compaction problems on the board exam. Covers problem setup (given data → identify question type), calculation sequence (γ_dry → RC or ZAV), result interpretation (pass/fail thresholds), and error checking (ZAV bounds). Typical exam scenario: field sample → RC calculation → pass/fail verdict.
Soil Compaction State Transitions
State diagram showing the progression of soil compaction from loose placement through dry side, optimum point, wet side, and saturation. Illustrates the physical change in state (γ_dry, void ratio, saturation) and practical concerns (dust, pore pressure, bearing capacity) at each stage. Reinforces why OMC is optimal and why wet-side compaction is problematic.
Typical Compaction Energy Distribution
Pie chart showing the relative compaction energy: Modified Proctor (~2700 kJ/m³) delivers ~4.5 times the energy of Standard Proctor (~600 kJ/m³). Visual reinforcement that Modified test is a significantly higher-energy process, hence higher γ_d,max and lower OMC.