Shallow vs. Deep Foundations, and Reading the Geotechnical Report

The first fundamental decision in foundation design is whether to use shallow or deep foundations. Shallow foundations (spread footings, strip footings, mat foundations) bear on soil or rock near the surface, transmitting building loads at relatively shallow depths — appropriate when competent soil with adequate bearing capacity exists near the surface and expected settlements are within acceptable limits. Deep foundations (driven piles, drilled piers, auger-cast piles) extend through weak near-surface soils to bear on deeper competent strata or develop capacity through skin friction along their length, and are required when weak soils, high loads, or strict settlement limits preclude shallow foundations.

The geotechnical report — boring logs, laboratory test results, and engineering recommendations — is the foundation for every foundation design decision. Read it for the soil conditions actually present, the test results used, and the assumptions made, not just the headline allowable bearing pressure; understanding the basis for the recommendation is essential for applying it correctly and for spotting conditions that need special attention.

Failure Modes in Bearing Capacity

A foundation fails in bearing when the applied load exceeds the soil's ability to resist without shear failure below the footing. Three modes are recognized:

  • General shear failure — a well-defined failure surface develops to the ground surface; heaving occurs on both sides. Typical of dense sands and stiff clays (relative density Dr > 67%).
  • Local shear failure — failure surface develops only partially; some heaving at the surface. Occurs in medium-dense sands and medium clays.
  • Punching shear failure — foundation punches through without a clear failure plane; occurs in loose sands and soft clays or under high embedment ratios.

Terzaghi's original equations apply to general shear; for local shear, Terzaghi suggested using 2c/3 and tan⁻¹(2tanφ/3) in place of c and φ.

Terzaghi's Bearing Capacity Equation

For a strip footing (B/L → 0) with general shear failure:

q_ult = c·Nc + q·Nq + 0.5·γ·B·Nγ

where c is cohesion (kPa), q = γ·Df is the overburden pressure at foundation depth Df, γ is unit weight of soil (kN/m³), B is footing width (m), and Nc, Nq, Nγ are dimensionless bearing capacity factors that depend solely on the friction angle φ':

  • Nq = e^(π tanφ) · tan²(45 + φ/2)
  • Nc = (Nq − 1) · cot φ (for φ > 0); Nc = 5.14 for φ = 0 (Skempton)
  • Nγ = 2(Nq + 1)tanφ (Meyerhof form) or 1.5(Nq − 1)tanφ (Hansen form)

Common tabulated values: at φ = 30°, Nc ≈ 30.1, Nq ≈ 18.4, Nγ ≈ 22.4. At φ = 35°, Nc ≈ 46.1, Nq ≈ 33.3, Nγ ≈ 48.0.

Meyerhof's Generalized Equation

Meyerhof extended Terzaghi to handle rectangular footings, inclined loads, and embedment above the footing level by introducing shape (s), depth (d), and inclination (i) correction factors:

q_ult = c·Nc·sc·dc·ic + q·Nq·sq·dq·iq + 0.5·γ·B·Nγ·sγ·dγ·iγ

Key correction factors (Meyerhof, also used in AASHTO LRFD Bridge Design Specifications):

  • Shape: sc = 1 + 0.2·(B/L)·Kp; sγ = 1 − 0.1·(B/L)·Kp (φ > 10°); where Kp = tan²(45 + φ/2)
  • Depth: dc = 1 + 0.2·(Df/B)·√Kp; dq = dγ = 1 + 0.1·(Df/B)·√Kp (φ > 10°)
  • Inclination: ic = iq = (1 − α/90°)²; iγ = (1 − α/φ)² where α is load inclination angle

Hansen's and Vesic's equations use slightly different factor formulations and are also accepted; AASHTO LRFD Article 10.6 specifically references them for bridge foundations.

Net vs Gross Bearing Pressure

The gross ultimate bearing capacity q_ult is the total pressure the soil can support. The net ultimate capacity q_net = q_ult − q subtracts the in-situ overburden stress that was already in equilibrium before construction. For ASD design, the allowable bearing pressure is:

q_allow = q_net / FS + q

Typical ASD factors of safety for bearing capacity range from FS = 2.5 to 3.0 for permanent loads. A FS of 2.0 may be acceptable when load is well-known and soil is well-characterized; FS = 3.0 is used when uncertainty is high.

LRFD Approach (IBC / AASHTO)

Under LRFD, the factored load effect must not exceed the factored resistance:

ΣηiγiQi ≤ φ·Rn

For geotechnical bearing resistance, AASHTO LRFD Article 10.5.5.2 specifies resistance factors φ_b ranging from 0.45 to 0.50 for spread footings on sand (SPT-based methods) and 0.35 to 0.40 for clay (Su-based). IBC Table 1806.2 lists presumptive allowable bearing pressures by soil description for cases where site-specific analysis is not performed — values range from 1,500 psf (75 kPa) for clay to 12,000 psf (575 kPa) for crystalline bedrock.

Water Table Effects

The water table directly affects the effective unit weight used in bearing capacity calculations. Three cases govern:

  • Water table at or above the base of the footing (depth Dw ≤ Df): use γ' = γsat − γw ≈ 9–10 kN/m³ for both the q term and the Nγ term.
  • Water table within B below the footing base (Df < Dw ≤ Df + B): use a linearly interpolated average unit weight for the Nγ term.
  • Water table deeper than B below the footing: no reduction needed for bearing capacity (though settlement analysis may still require buoyancy correction).

Foundation Types and Selection

Spread (isolated) footings support individual columns and are the simplest, most economical foundation type when soil conditions are adequate — footing size comes from dividing the column load (including footing self-weight and soil overburden) by the allowable bearing capacity. Combined footings support two or more columns when spacing is too tight for individual spread footings, and strap (cantilever) footings connect an interior column footing to an eccentrically loaded column near a property line with a rigid strap beam that balances moments and equalizes soil pressure. Strip footings (continuous wall footings) support bearing walls, typically sized for 1,000–2,000 psf bearing pressure on lightly loaded residential walls. Mat (raft) foundations cover the entire building footprint with a single reinforced concrete slab, distributing loads at reduced pressure and stiffening against differential settlement — appropriate when individual spread footings would cover more than 50–60% of the footprint (overlapping), when soil is variable, or when heavy loads demand very large footing areas; the mat is designed as an inverted floor slab with soil pressure as the "load" and column reactions as the "supports."

Special Conditions: Expansive Soils and Frost Heave

Expansive soils (predominantly CH and MH classification with swell pressure above 1,000 psf) can exert enormous pressure on foundations as they absorb water and expand — damage from expansive soils costs billions of dollars annually in the US, particularly in Texas, Colorado, Oklahoma, and California. Foundation options include drilled piers below the active zone of moisture fluctuation (typically 8–15 ft deep) with a void space under grade beams so the soil can heave without loading the structure; post-tensioned concrete slabs with perimeter beams designed to span across heaving soil; and chemical soil stabilization (lime or cement treatment) to reduce swell potential before construction.

Frost heave occurs when water in soil freezes and expands, lifting footings. Frost depth (the depth to which soil freezes in a 100-year extreme event) ranges from negligible in warm climates to 5–6 ft in northern Minnesota and New England, and all footings must bear below it to prevent frost heave from lifting the structure — a requirement that often governs minimum footing depth in cold climates regardless of bearing capacity.

Worked Example

A 2.0 m × 2.0 m square footing is founded at Df = 1.2 m in a dense sand with φ' = 33°, c' = 0, γ = 18 kN/m³. Water table is deep. Determine q_allow using FS = 3.0.

Step 1 — Bearing capacity factors at φ = 33°: Nq = 26.3, Nc = 38.6 (not needed for c = 0), Nγ = 32.2.

Step 2 — Shape factors (B/L = 1.0, Kp = tan²(61.5°) = 3.33): sγ = 1 − 0.1(1.0)(3.33) = 0.667; sq = 1 + 0.2(1.0)(3.33) = 1.667.

Step 3 — Depth factors (Df/B = 0.6, √Kp = 1.826): dq = dγ = 1 + 0.1(0.6)(1.826) = 1.110.

Step 4 — q_ult = q·Nq·sq·dq + 0.5·γ·B·Nγ·sγ·dγ = (18 × 1.2)(26.3)(1.667)(1.110) + 0.5(18)(2.0)(32.2)(0.667)(1.110) = 21.6 × 48.72 + 18 × 23.82 = 1,052 + 429 = 1,481 kPa.

Step 5 — q_net = 1,481 − 21.6 = 1,459 kPa; q_allow = 1,459/3.0 + 21.6 = 507 kPa (≈ 10,600 psf).

This is well above typical column loads, confirming that settlement, not bearing capacity, usually governs design in dense sand. See Consolidation and Settlement Analysis for the next step.