Foundations (Shallow and Deep) - Cheat Sheet
Your last-minute rapid-fire reference for shallow and deep foundation design, capacity calculations, and group behavior. Master the formulas, spot the traps, and solve exam problems in under 2 minutes per item.
SHALLOW FOUNDATIONS — Sizing & Basics
Formulas
A_req = P_service / q_a
Meaning
A_req = required footing area (m²); P_service = service load (kN); q_a = allowable bearing pressure (kPa)
Watch out
Use SERVICE loads, not factored/ultimate loads. Forget this and your footing will be undersized by 1.4–1.6×
When to use
Sizing isolated or combined footings; first step after soil investigation
B = √(A_req) for square footing
Meaning
B = footing width or side length (m); assumes square geometry
Watch out
Result is the ideal size; always round UP to the next practical dimension (e.g., 2.1 m → 2.2 m)
When to use
When problem asks for a square footing or equal L and B
L × B for rectangular footing, where L ≥ B
Meaning
Length × width; typically L:B ratio chosen for structural/architectural reasons
Watch out
Still must satisfy A_req; calculate minimum B first, then choose L to get A ≥ A_req
When to use
When footing must fit into a building grid or architectural constraint
Common values
Value
200–300 kPa
Symbol
q_a
Quantity
Allowable bearing, dense sand
Value
100–150 kPa
Symbol
q_a
Quantity
Allowable bearing, stiff clay
Value
50–75 kPa
Symbol
q_a
Quantity
Allowable bearing, soft clay (poor soil)
Value
0.9 m
Symbol
D_f (min)
Quantity
Minimum footing depth (NSCP 2015)
Value
2.5–3.0
Symbol
FS
Quantity
Typical factor of safety on bearing
Important facts
- Square footings are most economical (smallest perimeter for given area).
- Rectangular footings L:B ≤ 3:1 (ratios >3:1 increase stress concentration and settlement nonuniformity).
- Mat foundation when isolated footing area sum ≥ 50% of building footprint.
- Always check bearing capacity, settlement (elastic + consolidation), and structural design (shear, bending).
- Footing must rest on bearing stratum (not fill, topsoil, or organic material).
- Minimum depth D_f = 0.9 m (NSCP 2015); 1.2 m preferred in high-rise.
- Allowable bearing includes factor of safety (FS ≈ 2–3 on ultimate capacity) — it is NOT ultimate bearing.
Key definitions
Shallow Foundation
Example
A 2 m × 2 m column footing at 1.2 m depth is shallow; a 20 m-deep pile is deep.
A footing that transfers load to soil at or near ground surface (D_f < B, usually ~1–2 m deep); includes spread, combined, strap, and mat footings.
Mat/Raft Foundation
Example
A 10-storey building on soft clay uses a mat instead of 100 separate footings.
A large continuous footing covering most/all of the building footprint, used when soil is weak or individual footings would overlap (occupy >50% of footprint).
Allowable Bearing Pressure (q_a)
Example
Dense sand q_a ≈ 200–300 kPa; stiff clay q_a ≈ 100–150 kPa.
Maximum safe stress the soil can sustain under service loads; determined by geotechnical investigation (boring, lab tests) or code tables.
Footing Depth (D_f)
Example
Metro Manila: D_f ≈ 1.0–1.5 m typical for residential; deeper in flood-prone areas.
Vertical distance from ground surface to bottom of footing; must be ≥1 m (frost depth in temperate regions) and account for scour, fill removal.
Diagrams to know
- Isolated square footing: plan view (B × B), section (D_f depth, soil layers, water table).
- Mat foundation: plan showing column grid, section showing thickness variation.
- Combined footing for two columns: rectangular slab, load path from columns to centroid of footing.
- Strap footing: two separate footings tied by a stiff beam (strap) to equalize stress.
DEEP FOUNDATIONS — Pile Capacity (Single Pile)
Formulas
Q_u = Q_p + Q_s
Meaning
Q_u = ultimate pile capacity (kN); Q_p = end bearing (kN); Q_s = skin friction (kN)
Watch out
Q_u is ultimate; divide by FS (2.5–3.0) to get allowable Q_a. Do NOT add FS to individual Q_p and Q_s separately.
When to use
ALL pile capacity problems; foundational equation for deep foundations
Q_p = A_p × q_p, where q_p = c_u N_c* + q' N_q*
Meaning
Q_p = end bearing (kN); A_p = pile tip area (m²); c_u = undrained shear strength (kPa); q' = effective stress at tip (kPa); N_c* = 9 (deep pile in clay, NOT 5.7)
Watch out
N_c* = 9 for deep piles in clay (NOT the shallow footing value 5.14 or 5.7). Common exam trap: use wrong bearing factor.
When to use
End bearing in clay; typically N_c* ≈ 9 (fixed for deep piles)
Q_p = 9 c_u A_p (simplified for clay, ignoring overburden stress)
Meaning
Simplified form when overburden stress q' is small relative to c_u
Watch out
Only valid for clay with c_u >>q'; in deep piles or sand, must use full formula with N_q*
When to use
Quick hand calculation in clay; common in exam problems
Q_s (clay) = α c_u (π D) L
Meaning
Q_s = total skin friction (kN); α = adhesion factor (0.5–1.0, typically 0.7–0.9); c_u = undrained strength (kPa); π D = shaft perimeter (m); L = pile length (m)
Watch out
Use PERIMETER π D, not area. Forget π and your answer is off by 3.14×. Also, α varies: soft clay α ≈ 1.0, stiff clay α ≈ 0.7.
When to use
Skin friction in clay; α-method (adhesion method)
Q_s (sand) = ∑(K σ'_v tan δ × π D × dz) or Q_s ≈ K σ'_v(avg) tan δ (π D) L
Meaning
Q_s = skin friction in sand (kN); K = lateral earth pressure coefficient (0.5–1.0, typically 0.8); σ'_v = vertical effective stress (kPa); δ = pile-soil interface friction angle (≈0.5 to 0.8 φ); dz = depth increment
Watch out
Use effective stress σ'_v (not total), not undrained strength. δ is NOT φ; δ ≈ 0.5–0.8 φ.
When to use
Skin friction in sandy soils; β-method (stress method)
Q_a = Q_u / FS
Meaning
Q_a = allowable pile capacity (kN); FS = factor of safety (2.5–3.0 typical)
Watch out
FS ≈ 2.5–3.0 for piles; be sure problem states which FS to use. AISC 360 and ACI 318 may specify FS or use LRFD (φ factors).
When to use
Converting ultimate to allowable for design
Common values
Value
9
Symbol
N_c*
Quantity
N_c* for deep piles in clay
Value
0.8–1.0
Symbol
α
Quantity
Adhesion factor, soft clay
Value
0.5–0.7
Symbol
α
Quantity
Adhesion factor, stiff clay
Value
0.5–1.0 (typically 0.8)
Symbol
K
Quantity
Lateral earth pressure coefficient, sand
Value
0.5–0.8 × φ
Symbol
δ
Quantity
Interface friction angle, sand
Value
2.5–3.0
Symbol
FS
Quantity
Factor of safety, piles
Important facts
- Deep pile in clay: Q_p = 9 c_u A_p (N_c* = 9, not shallow footing value 5.14).
- Skin friction in clay dominates; in long, soft-clay piles, Q_s >> Q_p.
- Skin friction in sand: use effective stress σ'_v and K tan δ method.
- Adhesion factor α varies: 0.5–1.0 depending on clay stiffness; soft clay (higher α), stiff clay (lower α).
- Pile length L: longer piles have more skin friction; short piles (L/D < 10) rely more on end bearing.
- Downdrag (negative skin friction) occurs in consolidating soils: soil settles more than pile, dragging it down.
- Always apply FS ≈ 2.5–3.0 to Q_u to get allowable Q_a for service-load design.
Key definitions
End Bearing (Q_p)
Example
A 0.4 m diameter pile tip in clay c_u = 60 kPa: Q_p = 9 × 60 × 0.1257 ≈ 68 kN
Load carried by the pile tip pressing into soil at the pile base; depends on soil strength at depth and tip area.
Skin Friction (Q_s)
Example
0.4 m dia., 12 m long, clay c_u = 60 kPa, α = 0.9: Q_s = 0.9 × 60 × 1.257 × 12 ≈ 814 kN
Shear stress along the pile shaft transferred to surrounding soil; typically the dominant component in clay.
Ultimate Capacity (Q_u)
Example
Q_u = 68 + 814 = 882 kN
Total load at which the pile fails in shear/compression; sum of end bearing and skin friction.
Allowable Capacity (Q_a)
Example
Q_a = 882 / 2.5 = 353 kN (safe working load)
Safe design load = Q_u / FS; used for structural analysis and load rating.
Adhesion Factor (α)
Example
Soft clay α ≈ 1.0 (full strength mobilized); stiff clay α ≈ 0.6–0.7 (some slippage)
Ratio of pile-soil interface shear to undrained strength c_u; depends on clay rigidity (0.5–1.0).
Bearing Capacity Factors (N_c*, N_q*)
Example
Shallow footing N_c = 5.14; deep pile N_c* = 9 (deeper soil engagement)
Dimensionless coefficients for end bearing in clay and sand; N_c* ≈ 9 for deep piles (deep pile theory).
Diagrams to know
- Pile cross-section: diameter D, tip area A_p, perimeter π D, length L.
- Stress distribution along pile: skin friction f_s (kPa) vs depth, end bearing q_p at tip.
- Load-settlement curve: Q vs settlement, identifying Q_u (failure point) and Q_a (safe load).
- Negative skin friction diagram: soil settles more than pile → downward drag force on shaft.
PILE GROUPS — Efficiency & Block Failure
Formulas
Q_group = η × n × Q_single
Meaning
Q_group = ultimate group capacity (kN); η = group efficiency factor (≤ 1); n = number of piles; Q_single = single pile capacity (kN)
Watch out
DO NOT multiply single capacity by n alone. η < 1 because stress bulbs overlap; ignoring η is a major exam error.
When to use
All pile group problems; accounts for stress-zone overlap reducing efficiency
η = [1 + (n-1)/n × θ], where θ depends on pile spacing and soil
Meaning
η reduces with closer spacing (θ = angle of stress cone, ~20°–30° in clay); simplified formula for rectangular groups
Watch out
Various formulas exist (Converse-Labarre, Feld, etc.); use the one your course/code specifies. Problem often gives η directly.
When to use
Estimating η when not given; typical range η = 0.7–0.95 for pile groups
Block failure: Q_u,block = [c_u N_c* A_block + q' N_q* A_block] + perimeter friction
Meaning
Treats pile + surrounding soil as one large pier; check this capacity (often governs in clay)
Watch out
Block failure is a CAPACITY LIMIT; if block Q_u < group Q_u (sum), block governs. Overlook this and design is unsafe.
When to use
Clay piles: always check if block failure < individual pile sum; use lower value
Spacing criterion: s ≥ 3D (typical), where s = center-to-center distance, D = pile diameter
Meaning
Minimum spacing to reduce overlap and allow soil consolidation between piles
Watch out
Too-tight spacing (s < 2D) severely reduces η; too-loose spacing (s > 4D) wastes footprint.
When to use
Checking layout feasibility; tighter spacing (s = 2.5D) acceptable in sand, avoided in clay
Common values
Value
0.70–0.80
Symbol
η
Quantity
Group efficiency, clay (tight spacing)
Value
0.85–0.95
Symbol
η
Quantity
Group efficiency, sand (tight spacing)
Value
3D
Symbol
s
Quantity
Minimum pile spacing
Value
20°–30°
Symbol
θ
Quantity
Stress cone angle, clay
Important facts
- Group efficiency η decreases with tighter spacing and lower soil shear strength.
- In clay (lower friction), groups are less efficient (η = 0.7–0.85); in sand (higher friction), η = 0.85–0.95.
- Block failure is critical in clay; often the governing limit. Sand rarely shows block failure.
- Minimum spacing s = 3D; below 2.5D, significant capacity loss occurs.
- Large groups in soft clay may become mat-like in behavior; consider raft foundation instead.
- RA 544 (Geological Hazards Act) requires site characterization; geotechnical report must document pile capacity methodology.
Key definitions
Group Efficiency (η)
Example
A 3×3 group: η = 0.80 means the group carries 80% of (9 × Q_single), not 100%.
Ratio of actual group capacity to the sum of individual pile capacities; η < 1 because stress zones overlap.
Block Failure
Example
Soft clay, closely spaced piles: block capacity < group capacity; use block value for design.
Failure of the pile group + enclosed soil as a single large pier, not as individual piles; governs when pile-to-pile stress overlap is severe.
Pile Spacing (s)
Example
s = 3D standard; s = 2.5D tight; s = 4D very loose.
Center-to-center distance between adjacent piles; affects stress overlap and group efficiency.
Stress Bulb / Influence Zone
Example
Two piles 1.5D apart have overlapping bulbs in clay; stress from one pile reduces capacity of the other.
Zone around a loaded pile where significant stress increase occurs (~20°–30° cone angle in clay); overlapping bulbs reduce efficiency.
Diagrams to know
- Pile group plan: rectangular arrangement (2×2, 3×3, etc.), spacing s marked, load distribution.
- Stress bulb overlap: cone of stress around two adjacent piles, showing interference zone.
- Block failure envelope: pile group + surrounding soil treated as single column, sketching shear surface.
NEGATIVE SKIN FRICTION (Downdrag)
Formulas
Q_downdrag = f_s × A_shaft (downward load from consolidating soil)
Meaning
Q_downdrag = additional downward load (kN); f_s = negative skin friction stress (kPa, negative or downward); A_shaft = pile shaft area in consolidating zone (m²)
Watch out
Downdrag REDUCES net capacity; it adds load instead of helping. Ignore it and pile will fail under service loads.
When to use
When surrounding soil settles MORE than the pile (e.g., new fill, dredge fill, recent embankment)
Neutral depth = depth where pile and soil have equal settlement
Meaning
Above neutral depth: negative friction (downdrag); below: positive skin friction (support)
Watch out
Neutral depth depends on fill placement rate and soil consolidation; estimate from settlement analysis.
When to use
Identifying where downdrag zone ends; piles extend below neutral depth to gain capacity
Q_a,effective = Q_u - Q_downdrag - F_S
Meaning
Final allowable capacity accounting for downdrag reduction
Watch out
Do NOT simply subtract downdrag after applying FS; apply FS to (Q_u - downdrag).
When to use
Design of piles in consolidating soil (soft clay + recent fill)
Common values
Value
5–15 m
Symbol
d_neutral
Quantity
Typical neutral depth, coastal fill
Value
10–30%
Symbol
Q_downdrag / Q_u
Quantity
Downdrag as % of capacity
Important facts
- Downdrag is a MAJOR concern in coastal areas (dredge fill), reclaimed land, and new embankments on soft clay.
- Can reduce effective pile capacity by 10–30%; ignoring it is a serious design error.
- Downdrag zone typically extends from ground surface to neutral depth (estimated from settlement calculations).
- Piles in downdrag zones should extend well below neutral depth to gain support from stable soil.
- In Philippines: reclaimed land (Manila Bay, Subic), dredge-fill projects, and soft clay deposits all require downdrag checks.
- RA 9729 (Climate Change Act) emphasis on resilience; downdrag critical in climate-vulnerable low-lying areas.
Key definitions
Negative Skin Friction (Downdrag)
Example
Fill placed on soft clay → clay consolidates and settles more than pile → pile is dragged downward.
Downward shear stress exerted by consolidating soil on pile shaft; adds load instead of resisting it.
Neutral Depth (d_neutral)
Example
In a thick dredge-fill layer, neutral depth may be 5–10 m; piles must be long enough to reach below it.
Depth at which pile and surrounding soil have equal settlement; above = downdrag zone, below = normal skin friction zone.
Consolidating Soil
Example
Dredge fill, engineered fill, organic clay post-embankment — all susceptible to consolidation downdrag.
Soil undergoing settlement due to water drainage and grain compression, typically soft clay or recent fill.
Diagrams to know
- Downdrag profile: pile shaft, surrounding soil, neutral depth marked, downdrag zone shaded.
- Settlement curves: pile settlement vs soil settlement, intersection = neutral depth.
- Stress distribution: negative skin friction above neutral depth (downward arrows), positive below (upward arrows).
GEOTECHNICAL SITE INVESTIGATION & PILE SELECTION
Common values
Value
N = 30 → φ ≈ 36°
Symbol
N, φ
Quantity
SPT N → φ (dense sand)
Value
c_u ≈ 100(N - 1) kPa, e.g., N = 5 → c_u ≈ 400 kPa
Symbol
N, c_u
Quantity
SPT N → c_u (medium clay)
Value
2–3 m
Symbol
D_bore
Quantity
Minimum boring depth below footing
Value
3–5 boreholes, each 15–30 m deep
Symbol
N_holes
Quantity
Typical geotechnical report for medium project
Important facts
- RA 544 (Geological Hazards Act) & NSCP 2015 require geotechnical site investigation for all structures.
- Minimum boring: 3 holes, depths to ~5D below footing or pile tip; more for large/critical projects.
- SPT N-value correlations (tabulated in codes) → φ (sand), c_u (clay), bearing pressure estimates.
- Undrained strength c_u from vane shear, lab tests, or SPT-N correlation; essential for pile design.
- Water table location critical: affects effective stress, skin friction, downdrag potential.
- Pile materials: reinforced concrete (RC), steel H-piles, timber (rare now); choice affects capacity & corrosion.
- Corrosion allowance in marine/acid soil: subtract 3–5 mm from shaft diameter over 50+ year life.
Key definitions
Bore Log / Soil Profile
Example
0–2 m: fill; 2–8 m: clay N = 4, c_u = 30 kPa; 8–15 m: sand N = 20, φ = 35°.
Record of soil layers, depths, SPT N values, lab c_u and φ; foundation design is impossible without it.
Standard Penetration Test (SPT)
Example
Sand N = 10 → φ ≈ 28°; N = 30 → φ ≈ 36° (dense sand).
Field test: 63.5 kg hammer drop → 0.76 m, count blows N for 0.3 m penetration; correlates N to φ and soil type.
Undrained Shear Strength (c_u)
Example
c_u ≈ 100 × (N - 1) (soft to medium clay); vane shear test = direct measurement.
Shear strength of clay WITHOUT drainage; measured by vane shear, triaxial (UU), or estimated from N value.
Pile Type Selection
Example
Soft clay → long friction pile or bored shaft; dense sand → short pile or large-diameter caisson.
Choose based on soil profile: bored/drilled shafts in clay, driving piles in dense sand, friction piles in soft clay.
Diagrams to know
- Bore log profile: layers, depths, N values, water table, lab test results (c_u, φ, γ).
- SPT correlation charts: N vs φ (sand), N vs c_u (clay) for estimation.
- Soil profile for pile design: identify friction layer (skin friction zone) and bearing stratum (end bearing).
STRUCTURAL DESIGN OF FOUNDATIONS (RC/Steel) — Quick Reference
Formulas
Footing bending moment: M = 0.5 × q × (B/2)^2 per unit length
Meaning
q = bearing pressure (kN/m²); B = width (m); cantilever action from face of column to edge
Watch out
Assume uniform bearing stress q; if loads eccentric, stress is triangular (use adjusted q and M formulas).
When to use
Calculating flexural reinforcement in footings (ACI 318 Chapter 15)
Shear in footings: V_u = q × (B - b) × L, where b = column width
Meaning
One-way shear at d from column face; two-way (punching) at d/2 around column perimeter
Watch out
Distinguish one-way and two-way shear; two-way (punching) is more restrictive for thick footings.
When to use
Check shear capacity (ACI 318 Section 15.5); often governs footing thickness
Pile cap design: transfer column load to piles, check shear & bending (ACI 318 Chapter 15)
Meaning
Pile cap is a rigid footing distributing load to multiple piles; assume 45° stress strut model
Watch out
Cap must be thick enough to be rigid; assume load distributes at 45° from column to pile.
When to use
Designing pile caps with multiple piles
Common values
Value
0.5–0.75 m (isolated), 1.0+ m (combined, caps)
Symbol
h_min
Quantity
Minimum footing thickness
Value
~0.03 × f_y × d_b (for #5 bar in normal concrete)
Symbol
l_d
Quantity
Development length multiplier, ACI 318
Important facts
- ACI 318-19 (Section 15) governs footings: bending, shear, development of reinforcement.
- One-way shear at distance d from column face; two-way (punching) critical around perimeter.
- Use strength design (ultimate loads, φ factors) for reinforcement; check bearing at service loads.
- Reinforcement development length critical; minimum hooks and lap lengths per ACI 318.
- Footings on slopes require special detailing; check punching shear and moment due to slope geometry.
- Pile caps must be rigid (h ≥ 0.5–0.6 m typical); assume 45° strut action from column to piles.
Key definitions
Pile Cap
Example
For a 3×3 pile group, 2 m × 2 m cap, ~0.75–1.0 m thick, transferring load to 9 piles.
Reinforced concrete slab atop pile group, distributing column load to individual piles; must be rigid.
Bearing Pressure Distribution
Example
Square 2×2 m footing: q = P / 4 m²; if eccentric load, q_max and q_min vary.
In a footing, assumed uniform (simple design) or triangular (eccentric/moment cases); must not exceed q_a.
Diagrams to know
- Footing cross-section: column, bearing pressure q distribution, critical shear section at d, bending moment diagram.
- Pile cap plan & section: column, pile positions, critical load paths at 45° from column to piles.
- Reinforcement layout: bottom steel for tension in footing cantilever, top steel if moment reversal (backfill load).
Must remember
- Footing area A = P_service / q_a (use SERVICE loads, not factored). Undersizing is the #1 error.
- Pile Q_u = Q_p + Q_s. For clay: Q_p = 9 c_u A_p (NOT 5.14), Q_s = α c_u (π D) L. Remember perimeter π D, not area.
- Group capacity Q_group = η n Q_single (η < 1). Multiplying by n alone is a critical mistake; always reduce for overlap.
- Block failure in clay: check if (pile group + soil) acting as one pier is weaker than sum of individuals. Use lower capacity.
- Negative skin friction (downdrag) ADDS load in consolidating soils (soft clay + fill). Ignoring it → pile failure. Estimate neutral depth.
- Adhesion factor α varies: soft clay α ≈ 1.0, stiff clay α ≈ 0.5–0.7. Sand uses K σ'_v tan δ (effective stress, NOT undrained).
- Apply FS ≈ 2.5–3.0 to Q_u to get Q_a for service load design. Do NOT apply FS to Q_p and Q_s separately.
- Pile spacing s ≥ 3D; below 2.5D, efficiency drops sharply. Block failure governs in tight, weak-clay groups.
- Site investigation (bore log, SPT-N, c_u, φ) is non-negotiable; all capacity calculations depend on soil data. RA 544 requires it.
- Mat foundation when isolated footing area sum > 50% of building footprint or soil is very weak (q_a < 50 kPa).
Last minute tips
- PERIMETER vs AREA trap: Skin friction Q_s uses PERIMETER (π D), NOT cross-sectional area. Forgetting π D gives a wrong answer by 3.14×.
- N_c* = 9 for deep piles, NOT 5.14 (shallow footing). Board exams love this distinction; easy 5-point error if you mix them up.
- Group efficiency η: If problem doesn't give η, assume 0.75–0.85 for clay groups (tight spacing), 0.90–0.95 for sand. Safer to read problem carefully.
- Downdrag hits you in coastal/reclaimed land problems (dredge fill, soft clay). If problem mentions 'recent fill' or 'consolidating clay,' CALCULATE neutral depth and downdrag.
- Allowable vs Ultimate: q_a (shallow) and Q_a (deep) are DESIGN values (safe); Q_u and q_u are FAILURE values. Use FS correctly in conversion; don't double-count safety factors.
Comparison tables
Shallow vs Deep Foundations
| Aspect | Shallow Footing | Deep Foundation (Pile) |
|---|---|---|
| Depth | D_f < B, typically 1–2 m | D_f >> B, often 5–20+ m |
| Load mechanism | Bearing on soil at footing base | End bearing (tip) + skin friction (shaft) |
| Suitable soil | Medium/stiff clay, dense sand | Soft clay, weak soil; reaches firm strata |
| Cost | Cheaper (excavation simple) | Expensive (drilling/driving equipment) |
| Settlement | Often dominant issue (20–100 mm) | Usually <25 mm; less concern |
| Design formula | A = P / q_a | Q_u = Q_p + Q_s; Q_a = Q_u / FS |
| Exam focus | Bearing check, mat sizing, RC design | Capacity (clay vs sand), groups, downdrag |
Pile Capacity in Clay vs Sand
| Parameter | Clay (Undrained c_u) | Sand (Friction φ) |
|---|---|---|
| End bearing formula | Q_p = 9 c_u A_p (N_c* = 9) | Q_p = A_p (c + q' tan φ) N_q*; often c=0, so Q_p = q' N_q* A_p |
| Skin friction method | Adhesion (α-method): Q_s = α c_u π D L | Stress (β-method): Q_s = K σ'_v tan δ π D L |
| Q_s vs Q_p ratio | Q_s >> Q_p (long piles); e.g., 90% Q_s | Q_s ≈ Q_p (variable); e.g., 50–70% Q_s |
| Group efficiency η | Lower: 0.70–0.85 (stress overlap severe) | Higher: 0.85–0.95 (less overlap) |
| Block failure risk | HIGH; always check | Rare; usually individual pile governs |
| Downdrag risk | HIGH (consolidation-prone) | LOW (drainage is rapid) |
| Typical adhesion α / K | α = 0.6–1.0 (soft to stiff) | K = 0.5–1.0 (compact to dense) |
Bearing Capacity Factors: Shallow vs Deep
| Factor | Shallow Footing (D_f/B = 0.1–2) | Deep Pile (D_f/B >> 1) |
|---|---|---|
| N_c (clay bearing) | 5.14 (Terzaghi) to 5.7 (Meyerhof) | 9 (Deep pile theory) |
| N_q (sand bearing) | 0.4 to 2.5 (depth & friction) | Higher; depends on D_f/B ratio |
| N_γ (weight factor) | 0.0 to 0.8 (shallow), often neglected | Rarely used for piles |
| Key insight | Use footing bearing capacity equations (NSCP 2015 Section 9.4) | Use pile capacity (end + skin friction); N_c* = 9 fixed |
Diagrams
Foundation Types & Key Parameters
Overview of foundation categories, capacity formulas, and design approaches. Illustrates the hierarchical relationship between footing/pile types and their governing equations.
Pile Capacity Calculation Workflow
Step-by-step decision tree for single-pile capacity calculation: soil type → bearing & friction formulas → ultimate capacity → allowable (with FS and downdrag check). Critical path for PRC exam.
Shallow Foundation Sizing & Design Flow
Full workflow for shallow foundation design: area sizing → bearing check → settlement estimation → structural RC design. Shows decision points for footing type selection.
Pile Group Capacity Assessment
State diagram for pile group capacity assessment: single pile → spacing check → efficiency factor → group capacity → block failure check (clay) → final allowable. Shows logic for determining governing capacity.
Typical Pile Capacity Breakdown (Clay, Long Pile)
For typical long piles in clay (L/D > 20), skin friction dominates (≈90% of total), while end bearing contributes only ≈10%. This distribution shifts toward more end bearing for shorter piles or in sand.
Geotechnical Site Investigation Timeline
Chronological sequence of site investigation and design workflow. RA 544 requires completion of Phase 4 before foundation design. Each phase builds on prior data.