PE Geotechnical cheat sheet

SPT: 63.5 kg hammer, 760 mm drop, 51 mm OD split-spoon; drive 450 mm, discard first 150 mm seating, N is blows for the next 300 mm.

Energy correction: N60 = N × ER/60; a typical US safety hammer has ER near 60%.

Overburden correction: CN = (100/σ'v)^0.5 with σ'v in kPa, capped at about 2; (N1)60 = N60 × CN.

CPT measures qc, fs, and u; friction ratio Rf = fs/qc × 100, with high Rf generally indicating clay and low Rf indicating sand.

Thin-walled Shelby tubes with area ratio below 10% are used to obtain relatively undisturbed cohesive samples.

RQD = sum of intact core pieces 100 mm or longer divided by total run length × 100%; RQD below 25% is very poor rock.

Borehole methods: hand auger to about 3-5 m, hollow-stem auger with plug, and mud rotary for deeper holes; casing prevents collapse.

Standpipe piezometers indicate water level; vibrating-wire piezometers measure pore pressure; artesian head can cause base heave in excavations.

Atterberg limits: PI = LL − PL; LI = (w − PL)/PI; USCS classifies fine soil as CL if PI > 7 and above the A-line, and CH if LL ≥ 50.

Compaction energy: Standard Proctor about 600 kN·m/m³, Modified Proctor about 2700 kN·m/m³; relative compaction = γd(field)/γd(max) × 100.

Consolidation: Cc = Δe/log(σ'2/σ'1); cv is obtained by root-time or log-time construction; OCR = σ'p/σ'v0.

Mohr-Coulomb strength: τ = c' + σ' tanφ'; UU triaxial gives undrained shear strength, while CD triaxial gives drained c' and φ'.

Effective stress: σ' = σ − u; negative pore pressure in the capillary zone increases effective stress.

Darcy's law: v = k i; constant-head tests suit coarse soils and falling-head tests suit fine soils.

Unit weights: γsat = (Gs + e)γw/(1 + e); γd = γ/(1 + w); buoyant unit weight γ' = γsat − γw.

Relative density from (N1)60 in sand: loose below 15, medium dense 15-30, dense 30-50, very dense above 50.

Terzaghi strip footing: qu = cNc + qNq + 0.5γBNγ; square footing uses 1.3cNc and 0.4γBNγ terms.

Allowable bearing: qall = qult/FS, with FS typically 3; settlement often governs design over bearing capacity.

Eccentric footing: qmax,min = Q/A (1 ± 6e/B); e greater than B/6 produces partial contact and tension.

Elastic settlement: Se = qB(1 − ν²)If/Es; If depends on footing shape, embedment, and stiffness.

Pile capacity: Qult = Qtip + Qshaft; clay shaft resistance uses αsu and sand shaft resistance uses βσ'v.

Static pile load test: load typically applied to twice design load; Davisson or 10% diameter criteria define failure.

Drilled shafts: end bearing in rock or dense soil; base cleanliness is critical; slurry may be used to stabilize the hole.

Negative skin friction from settling fill or consolidating clay adds downdrag and reduces usable pile capacity.

Rankine coefficients: Ka = tan²(45 − φ/2) and Kp = tan²(45 + φ/2); active thrust for level backfill is 0.5γH²Ka.

At-rest pressure: K0 = 1 − sinφ for normally consolidated soil; K0,OC = K0,NC × OCR^0.5.

Retaining wall stability: overturning FS ≥ 2, sliding FS ≥ 1.5, bearing FS ≥ 3; passive resistance is included only if reliably mobilized.

Coulomb theory includes wall friction δ, which reduces active thrust and increases passive resistance.

Infinite slope with seepage parallel to the slope: FS = c'/(γz sinβ cosβ) + tanφ'/tanβ.

Method of slices: Bishop simplified satisfies moment equilibrium; Spencer satisfies both force and moment equilibrium.

Pseudo-static slope analysis applies horizontal seismic coefficient kh as a body force, reducing the factor of safety.

Drainage: hydrostatic pressure adds to wall load; weep holes and filters relieve water; clay backfill is avoided because of low permeability and swelling.

Liquefaction: CSR = 0.65(amax/g)(σv/σ'v)rd; FS = CRR/CSR, with CRR adjusted for (N1)60 and fines content.

Expansive clay: PI above 25 indicates high swell potential; lime or cement stabilization reduces plasticity and swell.

Frost heave requires freezing temperatures, frost-susceptible silt or fine sand, and capillary water; FSI ranks susceptibility.

Ground improvement: wick drains accelerate consolidation, stone columns increase bearing and drain, and deep soil mixing increases strength.

ASCE 7 site class A through F is based on Vs30, SPT resistance, or undrained shear strength; site class F requires site-specific analysis.

Compaction specification: 95% Standard Proctor is common for structural fill; pavement subgrade often requires 98% or higher.

Instrumentation: inclinometers detect lateral movement, piezometers monitor pore pressure, and settlement plates measure vertical displacement.

LRFD applies resistance factors φ below 1.0 to nominal resistance and load factors above 1.0 to loads.