Stresses in Soil Mass - Cheat Sheet
Your 30-minute emergency reference for effective stress, pore pressure, and stress increase calculations. Every formula, definition, and pitfall you need to ace geotechnical stress problems on the PRC exam.
Effective Stress Principle (Terzaghi's Law)
Formulas
σ = σ' + u → σ' = σ − u
Meaning
σ = total stress (kPa); σ' = effective stress (kPa); u = pore water pressure (kPa)
Watch out
Do NOT forget the minus sign. Pore pressure REDUCES effective stress. Below water table, u ≠ 0.
When to use
EVERY soil problem — effective stress governs strength and settlement, not total stress
σ = Σ(γᵢ × zᵢ)
Meaning
Sum of (unit weight × layer thickness) for all layers above the point of interest
Watch out
Use γ_sat (not γ_moist or γ_dry) BELOW the water table. Above WTM, use γ_moist or γ_nat.
When to use
Build total stress profile — always stack layers from surface downward
u = γ_w × z_w (hydrostatic)
Meaning
γ_w = unit weight of water (9.81 kN/m³ or ≈ 10 kN/m³); z_w = depth below water table (m)
Watch out
u = 0 above the water table. If seepage flow exists, add/subtract seepage pressure: u = γ_w(z_w ± i·z_seep).
When to use
Standard pore pressure calculation when there is no seepage
Common values
Value
γ_w = 9.81 kN/m³ (or use 10 kN/m³ in approximations)
Symbol
γ_w
Quantity
Unit weight of water
Value
γ_sat ≈ 19–21 kN/m³
Symbol
γ_sat
Quantity
Typical saturated unit weight (clay)
Value
γ_sat ≈ 19–20 kN/m³
Symbol
γ_sat
Quantity
Typical saturated unit weight (sand)
Value
γ_moist ≈ 16–18 kN/m³
Symbol
γ_moist
Quantity
Typical moist unit weight (above WTM)
Value
i_critical ≈ (γ_sat − γ_w) / γ_w ≈ 1.0–1.1
Symbol
i_critical
Quantity
Critical hydraulic gradient (quick condition)
Important facts
- Effective stress is INDEPENDENT of pore pressure path — only σ and u matter, not how water got there.
- Below the water table, ALWAYS use γ_sat, not γ_moist. Saturated unit weight includes all water in voids.
- Pore pressure u is ALWAYS non-negative below WTM (cannot be negative in hydrostatic conditions).
- Effective stress can INCREASE even if total stress stays the same if pore pressure DECREASES (e.g., drainage).
- In a two-layer system with different WTM in each layer, compute u separately for each layer.
- Quick sand occurs when σ' = 0, typically i_critical ≈ 1.0 to 1.1 for most natural soils.
- Effective stress principle applies to ALL soil types: sand, clay, silt — no exceptions.
- Seepage pressure is additive: u_total = γ_w·z_w + i·γ_w·z_seep (upward flow) or u_total = γ_w·z_w − i·γ_w·z_seep (downward).
Key definitions
Total Stress (σ)
Example
At 5 m depth in a clay layer (γ_sat = 20 kN/m³), σ = 20 × 5 = 100 kPa (if from surface).
Combined stress from soil weight and all external loads; includes both solid skeleton and pore fluid.
Effective Stress (σ')
Example
If σ = 100 kPa and u = 40 kPa, then σ' = 60 kPa — this is what the soil 'feels' and resists with.
Stress carried by the soil skeleton (grains); controls shear strength, compressibility, and bearing capacity.
Pore Water Pressure (u)
Example
At 3 m below water table, u = 9.81 × 3 ≈ 29.4 kPa (purely hydrostatic, no seepage).
Hydrostatic or dynamic pressure in the void spaces; acts equally in all directions (isotropic).
Water Table (WTM)
Example
If WTM is at 2 m depth, then at 4 m depth z_w = 2 m (not 4 m).
The depth at which pore pressure first becomes non-zero; u = 0 above, u > 0 below.
Seepage Pressure (i·γ_w·z_seep)
Example
Upward seepage (i > 0) INCREASES u and DECREASES σ'; can cause 'quicksand' condition if i_critical is reached.
Additional pore pressure caused by upward or downward groundwater flow; i = hydraulic gradient.
Quick Condition (Boiling Sand)
Example
i_critical ≈ (γ_sat − γ_w) / γ_w ≈ (20 − 9.81) / 9.81 ≈ 1.02 for typical saturated soil.
Occurs when upward seepage reduces σ' to zero; soil loses bearing strength suddenly.
Diagrams to know
- Total stress, pore pressure, and effective stress profiles (vertical plots) — σ vs depth, u vs depth, σ' vs depth.
- Soil layer stacking diagram showing γ above and below WTM with σ and u calculations.
- Seepage flow diagram with hydraulic gradient i and resulting pore pressure variation.
- Quick condition diagram showing σ' approaching zero as i approaches i_critical.
Stress Increase from Surface Loads
Formulas
Δσ (point) = (3Q) / (2πz²) × [1 / (1 + (r/z)²)]^(5/2)
Meaning
Q = point load (kN); z = depth below load (m); r = horizontal distance from load axis (m); Δσ = vertical stress increase (kPa)
Watch out
At r = 0 (directly below), formula simplifies to Δσ = 3Q / (2πz²). Do NOT forget the 3 or the 2π.
When to use
Boussinesq solution for a concentrated point load on the surface; use when r = 0 for directly below.
Δσ (point, r=0) = 3Q / (2πz²)
Meaning
Simplified Boussinesq at depth z directly below point load Q; Δσ decreases as z increases.
Watch out
This is an approximation; the full formula includes (r/z) ratio. Stress spreads at ~45° from point.
When to use
Direct stress increase below a concentrated load (pile point, column base, line load at one axis).
Δσ (2:1 method) = Q / [(B + z)(L + z)]
Meaning
Q = total load (kN); B = footing width (m); L = footing length (m); z = depth below footing (m); Δσ in kPa
Watch out
Load spreads to (B+z) × (L+z) at depth z, NOT B × L. Common mistake: using B × L area instead.
When to use
Quick approximation for rectangular footing on surface; assumes load spreads at 45° (2 vertical : 1 horizontal).
Δσ (strip load) = (q × B / π) × [θ + sin(θ)cos(2ϕ)]
Meaning
q = uniform load per unit area (kPa); B = strip width (m); θ, ϕ = angles (radians); used for uniform loads.
Watch out
Requires angle computations — use tables or Newmark's chart for practical problems.
When to use
For long, narrow uniformly loaded areas (e.g., embankment, long footing); more accurate than 2:1.
Common values
Value
3 / (2π) ≈ 0.477
Symbol
C_B
Quantity
Boussinesq coefficient (directly below point load)
Value
arctan(0.5) ≈ 26.57°
Symbol
θ
Quantity
Load spread angle (2:1 rule)
Value
I_z ≈ 0.5 to 1.0 (depends on B, L, z ratio)
Symbol
I_z
Quantity
Influence factor (footing center, shallow depth)
Value
r ≈ 2–3z (horizontal offset)
Symbol
r_neg
Quantity
Negligible stress increase distance
Important facts
- Boussinesq solution assumes elastic, semi-infinite, homogeneous soil — reasonable for most practical depths (z < 3B).
- Stress increase at depth z is proportional to Q and INVERSELY proportional to z² — spreads rapidly with depth.
- 2:1 method is conservative for clayey soils and reasonable for sandy soils; overestimates for very deep foundations.
- Stress increase from a point load becomes negligible beyond r ≈ 2–3z (horizontal offset 2–3 times the depth).
- Newmark's chart is accurate for any loaded area shape and position — preferred for complex layouts.
- For circular footings, stress increase is uniform over the loaded area (no edge effects for circular load).
- Stress increase is CUMULATIVE — multiple loads or adjacent footings must be superposed (added).
- Below the footing, Δσ is maximum at z = 0 (surface) and decreases with depth; no lateral spreading at z = 0.
Key definitions
Boussinesq Solution
Example
A 100 kN pile load at 2 m depth and 1 m offset causes Δσ ≈ 5.7 kPa (use full formula with r = 1, z = 2).
Closed-form solution for stress increase from a point load on a semi-infinite elastic medium; foundation for all load-spread methods.
2:1 Approximation
Example
A 3×4 m footing carries 1200 kN; at 2 m depth, Δσ = 1200 / [(3+2)(4+2)] = 1200 / 30 = 40 kPa.
Practical engineering rule assuming loads spread at 2:1 (vertical:horizontal slope) with depth — NOT exact but fast for design.
Influence Factor (Newmark)
Example
For a rectangular area corner, influence factor at depth z is lower than directly below center.
Dimensionless factor to multiply average load pressure; accounts for loaded area shape and position.
Stress Bulb
Example
Directly below a footing, σ ≈ average load pressure at z = 0, then decreases in a bulb shape with depth.
Vertical cross-section showing contours of constant stress increase; looks like an onion bulb or teardrop.
Pressure Distribution Angle
Example
At depth z = 2 m, a 2×2 m load spreads to (2+2)×(2+2) = 4×4 m area, spreading at ~27° from vertical.
The angle at which surface load spreads with depth; 2:1 rule assumes 26.57° (arctan 0.5) from vertical.
Diagrams to know
- Boussinesq stress distribution diagram showing Δσ vs r/z ratio for point load.
- 2:1 load spread diagram showing (B+z) × (L+z) expansion with depth z.
- Stress bulb diagram for surface footing — concentric contours of equal stress increase.
- Newmark's chart showing influence factors for rectangular areas at various depths and positions.
- Stress distribution from strip load (uniform pressure on infinite strip) — smooth decay with depth and lateral distance.
Pore Pressure and Seepage
Formulas
u = γ_w × z_w (no seepage)
Meaning
Pure hydrostatic pore pressure; z_w = depth below static water table
Watch out
If water table is NOT at surface, z_w is measured from water table, not from ground surface.
When to use
Default pore pressure calculation when groundwater is static (no flow).
u = γ_w × (z_w + i × L) (upward seepage)
Meaning
i = hydraulic gradient; L = seepage path length; upward flow INCREASES pore pressure.
Watch out
Upward seepage REDUCES effective stress and can trigger quick sand. i = Δh / L (head loss / path).
When to use
When groundwater flows upward (e.g., artesian, pumping near a well, beneath an embankment).
u = γ_w × (z_w − i × L) (downward seepage)
Meaning
Downward flow DECREASES pore pressure from hydrostatic value.
Watch out
Downward seepage INCREASES effective stress, improving stability but causing consolidation settlement.
When to use
When groundwater flows downward (e.g., infiltration from surface, drainage below a cut).
i_critical = (γ_sat − γ_w) / γ_w ≈ (γ' / γ_w)
Meaning
Hydraulic gradient at which effective stress becomes zero (quick condition); γ' = buoyant unit weight
Watch out
i_critical ≈ 1.0–1.1 for most soils. If i_actual > i_critical, soil loses bearing strength suddenly.
When to use
Check if upward seepage will trigger quicksand condition; compare i_actual to i_critical.
σ'_critical = 0 → i_critical = (γ_sat − γ_w) / γ_w
Meaning
At quick condition, effective stress is zero; soil behaves as liquid, no shear strength.
Watch out
Quick sand is a limit state — once triggered, boiling/piping occurs; prevent by reducing i or increasing γ'.
When to use
Design checks for embankments, excavations, and pumping situations with upward seepage.
Common values
Value
γ_w = 9.81 kN/m³
Symbol
γ_w
Quantity
Unit weight of water
Value
γ' ≈ 9–11 kN/m³
Symbol
γ'
Quantity
Typical buoyant unit weight (sand)
Value
γ' ≈ 9–12 kN/m³
Symbol
γ'
Quantity
Typical buoyant unit weight (clay)
Value
i_critical ≈ 1.0–1.1
Symbol
i_c
Quantity
Critical hydraulic gradient (typical soil)
Important facts
- Pore pressure is ALWAYS zero or positive in saturated soil (cannot go negative in hydrostatic conditions).
- Effective stress is REDUCED by upward seepage — can cause settlement, boiling, or piping.
- Downward seepage IMPROVES stability by increasing effective stress but may cause internal erosion if too steep.
- Critical hydraulic gradient i_critical ≈ 1.0 to 1.1 for most natural soils — depends on γ_sat and γ_w.
- Quick sand occurs when σ' = 0; at this point, shear strength τ = c' ≈ 0 (no friction, no cohesion).
- Seepage pressure follows the direction of flow — adds to u for upward flow, subtracts for downward flow.
- Water table can fluctuate seasonally — design must account for both high and low water table positions.
- In multi-layer soil, pore pressure profile can have kinks if permeability changes or flow direction changes.
Key definitions
Hydrostatic Pore Pressure
Example
At 4 m below water table with γ_w = 9.81 kN/m³, u = 39.24 kPa (purely from weight of water column).
Pore pressure in soil with no groundwater flow; u = γ_w × z_w below static water table.
Seepage Pressure
Example
Upward flow with i = 0.5 over 2 m path adds 0.5 × 9.81 × 2 ≈ 9.81 kPa to hydrostatic pressure.
Additional pore pressure (positive or negative) caused by groundwater flow through soil.
Hydraulic Gradient (i)
Example
If water level drops 1 m over a 2 m soil layer, i = 1 / 2 = 0.5 (downward seepage).
Ratio of head loss to seepage path length; i = Δh / L; dimensionless and always positive.
Buoyant Unit Weight (γ')
Example
If γ_sat = 20 kN/m³ and γ_w = 9.81 kN/m³, then γ' ≈ 10.19 kN/m³.
Submerged unit weight; γ' = γ_sat − γ_w; accounts for buoyancy of soil grains in water.
Quick Condition (Boiling, Piping)
Example
Sand deposit with i_critical = 1.02; if upward seepage i reaches 1.02, effective stress → 0, piping starts.
State where upward seepage reduces σ' to zero and soil behaves as liquid; occurs at i ≥ i_critical.
Artesian Pressure
Example
Water rising above ground level in a well — indicates positive artesian pressure; can cause uplift on foundations.
Pore pressure in a confined aquifer above the static water table at the surface; can cause uplift.
Diagrams to know
- Pore pressure vs depth diagram showing hydrostatic profile, upward seepage, and downward seepage cases.
- Effective stress reduction diagram showing σ' → 0 as i approaches i_critical (quick condition).
- Seepage flow diagram in soil with hydraulic gradient, water table, and pore pressure variation.
- Artesian well diagram showing confined aquifer with pore pressure above static water table.
- Boiling/piping diagram showing soil particles lifting during quick condition with zero effective stress.
Stress Profiles and Calculations
Formulas
Profile at depth z: σ(z) = Σ[γᵢ × Δzᵢ] + Δσ_external
Meaning
Layer-by-layer summation of stress; external loads (footing, embankment) add Δσ to geostatic stress.
Watch out
Layer boundaries can have discontinuities in σ if γ changes. Always use γ_sat below water table.
When to use
Build complete stress profiles combining initial (geostatic) stress with load-induced stress.
Geostatic stress: σ_v(z) = Σ(γᵢ × Δzᵢ) (no external load)
Meaning
Initial vertical stress from soil weight only; baseline before any footing or fill load.
Watch out
Must account for water table change with depth — use γ_sat, not γ_moist below WTM.
When to use
Starting point for all stress profiles; called 'in situ' or 'initial' stress.
Total stress increase from rectangular footing: Δσ_avg = Q / (B × L) (average, not point stress)
Meaning
Average vertical stress just below the footing contact area; not the same as point stress at depth.
Watch out
This is NOT the vertical stress profile — it is only the average at z = 0. Use Boussinesq or 2:1 for depth z > 0.
When to use
Quick first estimate of stress increase at footing level (z ≈ 0); used in bearing capacity.
Common values
Value
dσ/dz = γ (typically 16–21 kN/m³)
Symbol
γ
Quantity
Geostatic stress gradient in uniform soil
Value
z ≈ 3B to 4B (footing width B)
Symbol
z_eff
Quantity
Depth of significant stress increase influence
Value
Δσ ≈ 0 when r > 2–3z
Symbol
r_lim
Quantity
Stress increase falloff with lateral distance
Important facts
- Geostatic stress increases linearly with depth in a uniform layer; slope = γ.
- Stress profile changes slope at layer boundaries if γ changes (unit weight discontinuity).
- Below the water table, use γ_sat in stress profile; above WTM, use γ_moist or γ_nat.
- Load-induced stress (Δσ) decreases with depth; at great depth, Δσ becomes negligible (typically z > 3B).
- Effective stress profile typically has a kink at the water table if γ_moist ≠ γ_sat.
- Stress increase from load spreads laterally and vertically; use Boussinesq or 2:1 for any depth and offset.
- Multiple loads superpose: if 2 footings load the same point, their Δσ values ADD.
- Stress profile is always increasing with depth in the same layer (σ cannot decrease downward in hydrostatic case).
Key definitions
Geostatic Stress (Initial Stress)
Example
At 5 m depth in uniform soil (γ = 18 kN/m³), geostatic σ_v = 18 × 5 = 90 kPa.
Vertical stress from weight of soil above a point; no external load; baseline for all calculations.
Stress Profile
Example
A stress profile above the water table is linear (straight line); below WTM, it bends if γ_sat ≠ γ above.
Plot of σ, u, or σ' vs depth; shows how stress changes with depth in a soil deposit.
Load-Induced Stress (Δσ)
Example
A footing causes Δσ = 50 kPa at some depth; if geostatic σ = 100 kPa, total σ = 150 kPa.
Vertical stress increase from external loads (footing, embankment, pile); added to geostatic stress.
Superposition
Example
Two adjacent footings each cause Δσ = 30 kPa at a point; combined effect Δσ = 60 kPa (superposed).
Linear principle: total stress from multiple loads = sum of individual load stresses; valid for elastic soil.
Diagrams to know
- Complete geostatic stress profile (σ vs depth) for a multilayer soil with water table.
- Pore pressure profile (u vs depth) showing hydrostatic distribution and changes at WTM.
- Effective stress profile (σ' vs depth) showing variation above and below water table.
- Load-induced stress profile (Δσ vs depth) from footing — decays with depth using 2:1 or Boussinesq.
- Combined total stress profile (σ_geostatic + Δσ_load) showing effect of external load on depth.
- Stress path diagram (σ_v vs σ_h) used in advanced soil mechanics.
- Mohr's circle diagram showing stress state at a point in soil.
Must remember
- σ' = σ − u ALWAYS — effective stress is what matters for strength and settlement, NOT total stress. Below water table, pore pressure u REDUCES effective stress.
- Use γ_sat BELOW the water table, γ_moist ABOVE — this is the #1 source of student errors in stress profiles. Saturated soil is heavier.
- Boussinesq point load directly below: Δσ = 3Q / (2πz²) — not Q / (2πz²). The coefficient 3/(2π) ≈ 0.477 is critical.
- 2:1 method spreads load to (B+z) × (L+z) at depth z — NOT B × L. This is a 45° angle spread (2 vertical : 1 horizontal).
- Quick condition occurs when σ' = 0 during upward seepage — i_critical ≈ (γ_sat − γ_w) / γ_w ≈ 1.0 to 1.1. Prevent piping.
- Pore pressure u is measured from the WATER TABLE, not from the ground surface — if WTM is at 3 m depth, then at 5 m depth, z_w = 2 m (not 5 m).
- Upward seepage INCREASES pore pressure, DECREASES effective stress, reduces stability. Downward seepage DECREASES pore pressure, INCREASES effective stress, improves stability.
- Stress increase (Δσ) from loads DECREASES with depth and lateral distance — becomes negligible at z > 3–4 times the footing width B.
- Superposition principle: multiple loads' Δσ values ADD together at a point. If 2 footings both load a location, their stress increases combine.
- Layer boundaries in stress profiles show KINKS in the σ vs depth plot when γ changes — not smooth curves. Always mark these when drawing profiles.
Last minute tips
- ALWAYS CHECK THE WATER TABLE POSITION FIRST — this determines whether to use γ_moist or γ_sat, and where u = 0 starts becoming u > 0. A wrong water table depth ruins the entire stress profile.
- For any Boussinesq or 2:1 calculation, SKETCH the geometry (footing, load, point of interest) before calculating. This prevents sign errors and wrong assumptions about depth z and offset r.
- When building a stress profile in a multi-layer system with different WTM, STOP at the water table, recalculate u, and restart — do NOT assume linear continuation across WTM.
- If an exam problem mentions 'seepage,' 'piping,' 'boiling,' or 'artesian,' immediately CHECK whether i_critical is exceeded. If i_actual > i_critical, the answer is 'quick condition' or 'boiling' — σ' = 0.
- In comparative problems (e.g., 'compare effective stress before and after water table rise'), draw both profiles side by side. The difference in σ' is always u_difference — often the entire exam point hangs on recognizing this.
Comparison tables
Total Stress vs Effective Stress vs Pore Pressure
| Property | Total Stress (σ) | Effective Stress (σ') | Pore Pressure (u) |
|---|---|---|---|
| What it is | Sum of soil skeleton + water pressure | Stress carried by soil grains only | Water pressure in soil voids |
| Controls | Initial calculation (not used for strength) | Strength, settlement, consolidation | Water flow, pore pressure dissipation |
| Formula | σ = Σ(γᵢ × zᵢ) | σ' = σ − u | u = γ_w × z_w (+ seepage) |
| Above water table | σ = γ_moist × z | σ' = σ − u_capillary (if present) | u ≈ 0 (or negative if capillary) |
| Below water table | σ = γ_sat × z (from WTM down) | σ' = σ − γ_w × z_w | u = γ_w × z_w (hydrostatic) |
| Example at 5 m depth (WTM at 3 m, γ_sat = 20 kN/m³) | σ = 18(3) + 20(2) = 94 kPa | σ' = 94 − 9.81(2) = 74.4 kPa | u = 9.81(2) = 19.62 kPa |
Boussinesq vs 2:1 Method vs Newmark's Chart
| Method | Best For | Formula/Approach | Accuracy | When to Use | Limitation |
|---|---|---|---|---|---|
| Boussinesq Point Load | Concentrated loads (pile, column point) | Δσ = (3Q/2πz²) × [1/(1+(r/z)²)]^2.5 | High (elastic theory) | Single point or small loads at known location | Cannot easily superpose many loads; tedious for offsets |
| 2:1 Approximation | Rectangular footings, quick design | Δσ = Q / [(B+z)(L+z)] | Moderate (engineering approximation) | Fast footing stress at any depth | Does not account for footing stiffness; conservative estimate |
| Newmark's Chart | Any loaded area shape and position | I_z = influence factor from chart | High (empirical-analytical) | Complex footing shapes, multiple areas, edge stresses | Requires chart or table lookup; graphical method has reading error |
Hydrostatic vs Seepage Pore Pressure
| Condition | Pore Pressure Formula | Effective Stress Impact | Example Scenario | Critical Check |
|---|---|---|---|---|
| Static (no flow) | u = γ_w × z_w | σ' = σ − γ_w × z_w (normal reduction) | Lake, pond, or calm groundwater | u increases linearly; σ' stable |
| Upward seepage | u = γ_w × (z_w + i × L) | σ' DECREASES further; can reach 0 at i_critical | Below embankment, near pumping well, spring outlet | Check if i > i_critical; if yes, quick sand → boiling |
| Downward seepage | u = γ_w × (z_w − i × L) | σ' INCREASES; soil more stable | Drainage, infiltration, drying | u < hydrostatic; σ' improves but consolidation settlement |
| Critical condition | u approaches γ_w × z_w + i_critical × γ_w × L | σ' → 0; soil loses all shear strength | Artesian flow, uncontrolled piping, embankment toe seepage | σ' = 0 → immediate stability failure; prevent by design |
Soil Unit Weights — When to Use Which
| Unit Weight | Symbol | Value Range (kN/m³) | When to Use | Remember |
|---|---|---|---|---|
| Dry unit weight | γ_d | 13–17 | Laboratory consolidation, compaction (rarely in field stress profiles) | All void space is AIR; no water in voids |
| Moist (natural) unit weight | γ_nat or γ_moist | 16–19 | ABOVE the water table in field profiles | Soil has some moisture; partially saturated |
| Saturated unit weight | γ_sat | 19–21 | BELOW the water table in field profiles — ALWAYS use below WTM | All voids filled with water; heaviest unit weight |
| Submerged (buoyant) unit weight | γ' = γ_sat − γ_w | 9–12 | Effective stress calculations below water table; quick condition check | Net weight of soil particle in water; used in σ' analysis |
| Water unit weight | γ_w | 9.81 (≈10) | Pore pressure calculation; seepage pressure | Constant; use 9.81 kN/m³ or 10 kN/m³ approximation |
Diagrams
Stresses in Soil Mass — Complete Concept Map
Hierarchical breakdown of all stress concepts: total stress (from weight and loads), pore pressure (hydrostatic and seepage), effective stress (the controlling parameter), and methods to calculate stress increase. Central hub for exam review.
Effective Stress Calculation Procedure (Board Exam Step-by-Step)
Step-by-step decision tree for calculating effective stress at any depth, accounting for water table, seepage, and quick condition checks. Color-coded for safe (green) vs danger (red) outcomes. Use this algorithm in every exam problem.
Soil Stability States Under Seepage Conditions
State diagram showing soil stability transitions from static (hydrostatic) through seepage conditions. Illustrates how upward seepage degrades stability as hydraulic gradient i increases toward i_critical, eventually triggering quick sand failure. Use to understand failure mechanisms.
Selecting the Right Stress Increase Method (Δσ) — Decision Tree
Decision flowchart for choosing the correct formula (Boussinesq vs 2:1 vs Newmark) based on problem type and requirements. Avoids wasting exam time on wrong method; saves 5–10 minutes per problem.
Common Exam Error Distribution (Based on Board Feedback)
Pie chart showing the top 6 categories of student errors on past PRC exams. Prioritize review of the largest slices (unit weight confusion, pore pressure, formula coefficients). These account for >80% of lost points.