Isolated Pad Footings
Square/rectangular pads supporting individual columns. Efficient for discrete columns on competent soils. Check punching and eccentricity from column moments.
Shallow Foundations
Introduction of pad, strip, combined/strap and raft foundations — how they behave, how to design them, what to watch on site, and how modern practice evolved from Terzaghi’s bearing capacity theory.
When to use
- Moderate loads + competent near-surface soils
- Low groundwater or manageable dewatering
- Settlements within serviceability limits
When to reconsider
- Deep soft clays / organics, collapsible or expansive soils
- Adjacent sensitivity to differential settlement
- High uplift/lateral demands without restraint
Key checks
- ULS geotechnical: bearing, sliding, overturning
- ULS structural: punching, shear, flexure
- SLS total & differential settlement, angular distortion, durability & groundwater effects
Overview
Shallow foundations transfer structural actions to near-surface soils by distributing load over sufficient area to (i) avoid shear failure and (ii) limit total/differential settlement. Layout should anticipate property boundaries, utilities, staged construction, and tolerance management.
Design inputs: ground investigation (borehole logs, lab tests, in-situ tests, groundwater), characteristic parameters
(γ, c′/cu, φ′, E, mv, k), design actions (N, V, H, M, uplift), load cases/combinations, durability class,
and construction constraints. Distinguish between total-stress and effective-stress parameters according to the design situation.
Types of Shallow Foundations
Strip Footings
Continuous along walls or closely spaced columns. Good for masonry/basement walls; controls differential settlement along the wall line.
Combined Footings
Single footing supporting two columns when spacing/boundaries preclude separate pads. Proportion so the resultant passes through the footing centroid.
Strap Footings
Two pads tied by a rigid strap; re-balances pressures where an exterior column cannot be centered (e.g., near a boundary).
Raft (Mat) Foundations
Large slab supporting many columns/walls; reduces contact pressure and differential settlement on weak/variable soils. Consider soil–structure interaction and non-uniform subgrade reaction rather than assuming a uniform pressure distribution.
How They Work
- Stress distribution: Contact pressure & stress bulbs diminish with depth; failure surfaces mobilize soil shear strength.
- Failure modes: General shear (dense/strong soils), local shear (loose/soft, often treated via reduced φ/c or N-factors), punching under concentrated loads or thin mats.
- Settlement: Immediate (elastic), primary consolidation in saturated fines, secondary compression; angular distortion and differential settlement often govern serviceability.
- Eccentric/inclined loading: Non-uniform pressures; ensure
e_x \le B/6ande_y \le L/6for compression-only bearing, otherwise base the check on the effective compression area.
Geotechnical Design
Ultimate Bearing Capacity
For a strip footing at depth Df on homogeneous soil:
qu = c Nc sc dc ic bc +
q Nq sq dq iq bq +
0.5 γ B Nγ sγ dγ iγ bγ
- q = γ' Df (effective overburden); B footing width; γ' effective unit weight.
- Nc, Nq, Nγ from φ (total-stress or effective-stress as appropriate); use Meyerhof/Hansen/Vesic charts or code annexes.
- Correction factors: shape (s), depth (d), load inclination (i), base/ground (b) as applicable; for square/circular footings shape factors are more significant.
- For local shear (loose/soft), reduce c, φ or use reduced N-factors.
Apply groundwater corrections to effective stresses; adjust γ and surcharge q for submerged conditions and shallow water tables.
Settlement Assessment
- Immediate: elastic theory (e.g. Boussinesq-based influence factors) using E or G and Poisson’s ratio; for layered soils, evaluate layer-wise and sum contributions.
- Primary consolidation (clays): 1D settlement
S = H Δσ' mvor e–log σ′ methods using Cc, Cr. - Secondary compression:
Ss = Cα H log(t/tp)where relevant. - Differential & angular distortion: compare with project-specific tolerance criteria; consider raft stiffness, soil variability, and the consequences of serviceability performance.
Sliding, Uplift & Eccentricity
- Sliding: let H be the design horizontal action at the base; check
H \le (N' \tan φ' + c' A)with appropriate partial factors on actions and resistances and consistent drainage assumptions. - Uplift: include self-weight, overburden, and any tension piles/anchors if present; consider buoyancy & hydrostatic uplift.
- Eccentricity: use effective bearing area Aeff via the “middle-third” rule; average pressure
q = N/Aeffand linear distribution checks, noting that tension zones require more advanced treatment.
Structural Checks
Punching & One-way Shear
Verify perimeter-dependent punching around columns for pads/rafts and one-way shear at code-defined critical sections (typically at d-to-2d from faces). Increase thickness or add shear reinforcement as needed.
Flexure & Cracking
Design top/bottom reinforcement for hogging/sagging regions; control crack widths per exposure class and cover requirements. Ensure the assumed soil pressure distribution in structural design is compatible with the geotechnical model.
Construction Considerations
- Founding level QA: inspect bearing surface; remove soft spots; blinding if required; record chainage/levels and observed strata.
- Groundwater: sump/wellpoint systems; avoid prolonged drawdown; monitor adjacent ground and structures for settlement.
- Concrete: appropriate durability class; slump/strength testing; curing; joint detailing for rafts/strips.
- Backfill: layer thickness, compaction targets, and protection of drainage/waterproofing membranes.
- Safety & environment: trench support, contamination handling, spoil management, noise/vibration controls; consider monitoring (e.g. settlement markers, inclinometers) where risk justifies it.
Terzaghi Equations & Further Development
Terzaghi’s bearing capacity expression for strip footings provided the seminal framework using Nc, Nq, Nγ. Meyerhof expanded to include inclination/shape/base factors, Brinch Hansen offered unified expressions with explicit factors and local-to-general shear treatment, and Vesic refined N-factors and deformation considerations. Modern codes embed these within partial-factor formats.
Allowable Design vs Limit State Method
| ASD (Working Stress) | Limit State (LRFD) | |
|---|---|---|
| Safety format | Global factor on capacity | Partial factors on actions, materials, resistance |
| Checks | Allowable bearing + settlement limits | ULS (bearing/sliding/overturning) and SLS (settlement, deformation) |
| Pros | Simple, familiar | Consistency with reliability targets; nuanced uncertainty handling |
| Notes | One global margin; often retained only for minor or legacy works | Requires careful selection of characteristic values and factors per code; prevailing format for major structures |
Worked Example (Sketch)
Given: Square pad, B = 2.0 m, Df = 1.5 m, sand (φ = 32°, c ≈ 0), γ = 19 kN/m³, Nq=18.4, Nγ=15.1. Load Nk= 2500 kN (incl. self-weight approx later). Use ASD with FS=3.
- Surcharge: q = γDf = 19×1.5 ≈ 28.5 kPa (adjust to γ′ if groundwater is relevant).
- Ultimate (strip-base form, adapt for square via shape factors):
qu ≈ qNq + 0.5γBNγ = 28.5×18.4 + 0.5×19×2.0×15.1 ≈ 524 + 287 ≈ 811 kPa.
With square shape factors (≈1.2 for Nq term, ≈0.6–0.8 for Nγ depending on source), adjust accordingly. - Allowable net: qa,net ≈ (qu/FS) − q ≈ (811/3) − 28.5 ≈ 270 − 28.5 ≈ 240 kPa (before shape/depth/inclination refinements).
- Area check: A = B² = 4.0 m² → Allowable load ≈ (qa,net + q)×A ≈ (240+28.5)×4 ≈ 270×4 ≈ 1080 kN → still insufficient for 2500 kN ⇒ increase B and re-check or switch to raft/deep foundations.
- Next steps: iterate B (updating bearing and settlement for each trial size), check punching and sliding, and consider raft or piled solutions to control settlement and differential movement.
Numbers are illustrative; use your project’s governing standards, groundwater conditions, and calibrated N-factors and soil parameters.