Geotechnical Engineering — Soil Properties, Foundations, Retention, Stability

Geotechnical engineering treats soil + rock as engineering materials: characterising in-situ behavior, predicting deformation + strength + drainage under structural loads, and designing the foundations, retaining systems, slopes, and ground improvements that connect built works to the earth. This note expands beyond soil-mechanics into the deep end: site investigation programs, in-situ + lab testing, shallow + deep foundations, earth retention, slope stability, seismic geotech (liquefaction + sliding-block analysis), and the modern numerical-analysis stack (PLAXIS, FLAC, SLIDE, GeoStudio). References: ASCE 7-22, IBC 2024 Chapter 18, AASHTO LRFD Bridge Design Specifications 9th ed 2020, EN 1997-1 Eurocode 7, FHWA-NHI + FHWA-HRT technical-publication series, DM-7.01 + DM-7.02 NAVFAC.

1. Soil classification

1.1 USCS — Unified Soil Classification System

Per ASTM D2487. Two-letter symbol indicating major component + secondary descriptor:

Coarse-grained (> 50 % retained on No. 200 / 0.075 mm sieve):
- G gravel — > 50 % of coarse fraction retained on No. 4 (4.75 mm).
- S sand — > 50 % of coarse fraction passes No. 4.
- Secondary letter: W well-graded (Cu > 4 G or > 6 S; 1 < Cc < 3), P poorly graded, M silty fines, C clayey fines.
Fine-grained (≥ 50 % passes No. 200):
- M silt, C clay, O organic.
- Plasticity: L low (LL < 50), H high (LL ≥ 50).
Coefficient of uniformity Cu = D60/D10; coefficient of curvature Cc = D30²/(D10·D60). Both from GSD curve.

Group symbols + names: GW, GP, GM, GC, SW, SP, SM, SC, ML, CL, OL, MH, CH, OH, Pt (peat).

1.2 AASHTO Soil Classification

Per AASHTO M 145. Highway-engineering oriented. Seven groups A-1 to A-7 + subgroups (A-1-a, A-1-b, A-2-4, A-2-5, A-2-6, A-2-7, A-7-5, A-7-6).

Group Index (GI) = [F − 35](0.2 + 0.005(LL − 40)) + 0.01(F − 15)(PI − 10), where F = % passing No. 200.
A-1 + A-3 = granular, excellent subgrade. A-7-6 = highly plastic clay, poor subgrade.

1.3 USDA Soil Texture Classification

Triangle of sand + silt + clay percentages. Used for agronomy + erosion + agricultural drainage; less common in foundation design but appears in environmental + landfill specs.

1.4 Visual + manual identification

ASTM D2488 — visual-manual identification. Color (Munsell), moisture, plasticity (toughness, ribbon), dilatancy (Beaver-tail test), dry strength, gradation. Critical for field logging.

2. Index + state properties

2.1 Atterberg limits

Per ASTM D4318. Plastic limit PL, liquid limit LL, plasticity index PI = LL − PL.

Casagrande LL device — closed-groove apparatus; 25 blow closure defines LL. Multi-point + one-point methods.
Fall-cone LL — 80 g 30° cone, 20 mm penetration in 5 s — preferred in EU + Asia per BS 1377 + ISO 17892-12.
Plasticity chart: A-line PI = 0.73(LL − 20) divides CL/CH from ML/MH. U-line PI = 0.9(LL − 8) upper bound on plotted soils.

Activity Ac = PI / (% clay < 2 µm). Skempton 1953 — inactive (< 0.75 illite/quartz), normal (0.75–1.25 illite/montmorillonite mixtures), active (> 1.25 sodium montmorillonite/bentonite).

2.2 Grain-size distribution (GSD)

Per ASTM D6913 (sieve, > 75 µm) + ASTM D7928 (hydrometer, < 75 µm). Output: % passing vs grain size log-plot. Characteristic diameters: D10 (effective size — Hazen 1911), D30, D50, D60.

Hazen permeability k ≈ 100 D10² (k in cm/s, D10 in cm) — gives order of magnitude for clean sands.

2.3 Void ratio + porosity + saturation

Void ratio e = Vv / Vs (volume voids / volume solids). Typical 0.4–1.0 sands, 0.3–1.5 clays, 5–25 peats.
Porosity n = Vv / V = e / (1 + e). Typical 0.25–0.55.
Saturation S = Vw / Vv (water/voids). 0 dry, 1.0 saturated.
Water content w = Mw / Ms (mass-based, %).
Unit weights: dry γd = Gs · γw / (1 + e); saturated γsat = (Gs + e) · γw / (1 + e); buoyant γ’ = γsat − γw. Gs (specific gravity solids) typical 2.65–2.80 silica/quartz; 2.7–3.0 clays.

2.4 Relative density + compactness

Relative density Dr = (emax − e) / (emax − emin) — granular soils. Dr = 0 % loose, 35 % medium dense, 65 % dense, 85 % very dense. Per ASTM D4253 + D4254.
Standard Proctor + Modified Proctor compaction (ASTM D698 + D1557) — defines maximum dry density at optimum moisture content (OMC). Standard 12,375 ft-lb/ft³ (600 kN·m/m³); Modified 56,250 ft-lb/ft³ (2700 kN·m/m³).

3. Effective stress + permeability

3.1 Terzaghi effective stress

Karl Terzaghi 1925 — effective stress σ’ = σ − u. The single most important concept in geotechnical engineering. Soil mechanical behavior governed by σ’, not total stress σ. Pore water pressure u = γw · zw (hydrostatic for steady state).

In partially saturated soils, Bishop (1959) generalized: σ’ = (σ − ua) + χ(ua − uw), where χ depends on degree of saturation.

3.2 Permeability + Darcy’s law

q = k · i · A, where i = hydraulic gradient = Δh / L. Permeability k:

Gravel: 10⁻¹ to 10² cm/s
Sand: 10⁻³ to 10⁻¹ cm/s
Silt: 10⁻⁶ to 10⁻³ cm/s
Clay: 10⁻¹⁰ to 10⁻⁷ cm/s

Tests: constant-head permeameter (ASTM D2434) for k > 10⁻⁴; falling-head for k 10⁻⁷ to 10⁻⁴; triaxial flexible-wall (ASTM D5084) for clays; field pump tests (ASTM D4050) for aquifer-scale k.

3.3 Seepage + flow nets

Laplace equation for steady-state confined seepage. Hand-drawn flow nets (Casagrande 1937) or numerical via SEEP/W, PLAXIS Flow, MODFLOW.

4. Consolidation

4.1 1D Terzaghi consolidation

Saturated clay layer under load — excess pore pressure dissipates over time, transferring load to soil skeleton. Governing PDE: ∂u/∂t = Cv · ∂²u/∂z². Coefficient of consolidation Cv [length²/time], typical 0.01–10 m²/yr for normally consolidated clays.

Standard 1D oedometer (consolidometer) test per ASTM D2435:

Load increments (LIR = 1; each step doubles vertical effective stress).
24-hr duration each.
Output: void ratio vs log effective stress (e-log σ’ curve), Cc compression index (slope of NC line), Cr recompression index (slope of unload-reload).
Casagrande construction for preconsolidation pressure σ’p — bisect max-curvature angle + project to NC line.
t50 + t90 methods for Cv: log-time (Casagrande) at t50 = 0.197·H²/Cv; root-time (Taylor) at t90 = 0.848·H²/Cv. H = drainage path length.

Time-rate: U = average degree of consolidation; U = 50 % requires Tv = 0.197 (Tv = Cv · t / H²). U = 90 % requires Tv = 0.848. U = 99.4 % at Tv = 2.0.

4.2 Secondary compression

Cα = Δe / Δlog t — creep settlement after primary consolidation. Mesri + Castro 1987 — Cα / Cc ≈ 0.04 ± 0.01 inorganic clays, 0.05 ± 0.01 organic, 0.075 ± 0.01 peat. Cα independent of stress level + drainage path length.

4.3 Skempton A + B pore pressure coefficients

Skempton 1954: Δu = B[Δσ3 + A(Δσ1 − Δσ3)]. B = 1 for saturated soil (incompressible water), < 1 for partially saturated. A depends on stress history: A ≈ 0.7 NC clay, 0–0.3 OC clay, > 1 sensitive clay.

4.4 Schmertmann elastic settlement for sands

Granular soils don’t follow consolidation theory — settlement is essentially instantaneous + elastic. Schmertmann 1970 + 1978: s = C1 · C2 · Δp · Σ(Iz / Es) · Δz over multiple sub-layers. C1 = embedment correction, C2 = creep correction, Iz = strain influence factor (triangle peaking at 0.5B–B below footing, ~0.6 magnitude). Es from CPT (Es ≈ 2.5 qc square; 3.5 qc rectangular).

Hough method (1959) — empirical N-value-based settlement for sands. Burland + Burbidge 1985 — refined SPT-based correlations for sands.

5. Shear strength

5.1 Mohr-Coulomb failure criterion

τf = c’ + σ’ · tan φ’ (effective stress) — drained. τf = Su (undrained) — total stress, applicable to saturated clays in undrained loading.

φ’ typical: dense sand 38–46°, loose sand 28–34°, NC clay 18–30°, OC clay 20–28°. c’ typical: clean sand ~0, silt 0–10 kPa, NC clay 0–10 kPa, OC + cemented clays 10–50+ kPa.

5.2 Drained vs undrained behavior

Loading rate vs consolidation time governs whether pore pressures generate. Fast loading on low-permeability clay → undrained response (constant volume; Su parameter). Slow loading or granular soil → drained (effective stress; c’ + φ’).

Undrained shear strength Su of clays:

Normally consolidated: Su / σ’v ≈ 0.22 (Mesri 1975 + 1989) to 0.25 (Skempton 1957). Critical for embankment + cut design.
Overconsolidated: Su / σ’v = (Su / σ’v)NC · OCR^0.8 (Ladd + Foott 1974 SHANSEP).

5.3 Laboratory shear tests

Direct shear (ASTM D3080) — granular soils + frictional interfaces. Force shear plane horizontally; no pore-pressure measurement. Strain-controlled.
Triaxial UU (Unconsolidated Undrained, ASTM D2850) — undrained Su of saturated clay. No consolidation; no drainage; quick (~10 min).
Triaxial CU (Consolidated Undrained, ASTM D4767) — consolidate to specified σ’c then shear undrained; measure pore pressure. Gives effective stress (φ’, c’) + undrained strength at OCR.
Triaxial CD (Consolidated Drained, ASTM D7181) — drainage allowed; long duration (days to weeks for clays). Gives effective stress parameters directly.
Direct simple shear (DSS) — Norwegian Geotechnical Institute design; constant-volume condition for undrained tests; closer to embankment + slope failure-surface stress state than triaxial.
Ring shear — large-displacement residual strength φ’r for back-analysis of landslides on reactivated surfaces.

5.4 Normally + overconsolidated behavior

NC (OCR = 1) — current σ’v ≥ all past loads. Critical-state line + NCL passing through stress history. Volume decreases on shearing (contractive).
OC (OCR > 1) — soil has been at higher stress historically; recompression curve at low σ’v. Dilative on shearing if OCR > ~2. Strong + stiff at low σ’v.

6. In-situ testing

6.1 Standard Penetration Test (SPT)

Per ASTM D1586. 51-mm OD split-spoon driven by 64-kg hammer dropping 762 mm. Record blows per 150-mm increment for 450 mm; N-value = blows for middle + bottom 300 mm.

Energy efficiency: Donut hammer 45 % ER, Safety 60 %, Automatic 80–90 %. Correct to N60 = N · ER / 60.

Overburden correction: N1,60 = N60 · CN, where CN = (1 / σ’v)^0.5, σ’v in atm. Cap CN ≤ 1.7.
Density correlation (sands):
- N1,60 < 4 very loose; 4–10 loose; 10–30 medium dense; 30–50 dense; > 50 very dense.
Undrained strength (clays) — Terzaghi-Peck 1948: Su ≈ 6·N kPa. Weakly correlative; SPT is poor in cohesive soils.

SPT remains the dominant US site-investigation tool despite known limitations — universally available, decades of empirical correlations.

6.2 Cone Penetration Test (CPT) + CPTu

Per ASTM D5778. 36-mm-diameter, 60° cone pushed at 20 mm/s. Records:

qc cone tip resistance (MPa).
fs sleeve friction (MPa).
u2 pore-pressure behind shoulder (CPTu / piezocone) (kPa).

Friction ratio Rf = fs / qc × 100 %. Robertson 1990 + Robertson 2009 SBT chart (soil behavior type) — qc / pa vs Rf locates soil class.

Advantages over SPT: continuous profile (every 20 mm), no sample disturbance, repeatable, identifies thin seams. Disadvantages: no sample, refusal in dense gravel, equipment ~ $3M.

Equipment: Vertek Hogentogler 20-ton + 30-ton truck-mounted (Lebanon NH), Geomil + A.P. van den Berg + Pagani + Gouda CPT rigs, In-Situ Engineering + ConeTec Investigations + Gregg Drilling (West Coast US) + Fugro (offshore + global).

6.3 Dilatometer (DMT)

Marchetti dilatometer, Silvano Marchetti 1980 Italy. 95 × 15 mm flat blade with 60-mm membrane. Push to depth, inflate membrane in two stages (A + B pressures). Compute material index Id, horizontal stress index Kd, dilatometer modulus Ed. Empirical correlations to OCR, K0, undrained strength, drained friction, settlement modulus.

6.4 Vane shear test

ASTM D2573. Four-bladed vane (50 × 100 mm typical, H/D = 2) pushed below borehole base + rotated. Torque to failure → Su of sensitive + soft clays. Bjerrum 1972 correction µ for PI: µ ≈ 1 − 0.0033(PI − 20) for embankment back-analysis.

6.5 Pressuremeter (PMT)

Ménard pressuremeter (Louis Ménard 1957 France). 70-mm probe in 76-mm prebored hole; inflate radially; pressure-volume curve. Limit pressure pL + Ménard modulus EM. Common in Europe; basis of French foundation design (Fascicule 62-V).

Cambridge SBP self-boring pressuremeter — installs without disturbance; research-grade.

6.6 Other in-situ tests

Plate load test (ASTM D1194) — direct bearing capacity + modulus of subgrade reaction k.
California Bearing Ratio (CBR) (ASTM D1883 lab, D4429 field) — pavement subgrade strength.
Geophysical — seismic refraction + reflection, MASW (Multichannel Analysis of Surface Waves) for shear-wave velocity profile, electrical resistivity (ER), ground-penetrating radar (GPR).

7. Site investigation

7.1 ASTM standards

ASTM D420 Standard Guide for Site Characterization.
ASTM D5434 Field Logging of Subsurface Explorations of Soil + Rock.
ASTM D5079 Preservation + Transportation of Rock Core Samples.
ASTM D6066 Determining Normalized Penetration Resistance of Sands for Liquefaction Evaluation.

7.2 Boring layout + depth

Spacing: typical 30 m grid for buildings; tighter for high-mast loads or known variability.
Depth: to the lesser of (a) 1.5× building width below founding level, (b) bedrock, or (c) depth at which stress increase < 10 % of in-situ.
Number: AASHTO LRFD guidance — minimum 1 boring per substructure unit for bridges; commercial buildings typically 1 per 20–40 m grid spacing or per major column line.

7.3 Drilling methods

Hollow-stem auger — most common shallow; soft to medium soils; min ~7.5 m depth.
Mud-rotary — dense soils + below water table; bentonite + polymer drilling fluids.
Sonic drilling — high-resolution continuous core; expensive; contaminated-sites + research.
Rock coring — NQ / HQ (47.6 / 63.5 mm) diamond bits; ASTM D2113.

8. Shallow foundations

8.1 Bearing capacity — Terzaghi 1943 + extensions

Ultimate bearing capacity equation: qult = c · Nc + q · Nq + 0.5 · γ · B · Nγ

Plus shape, depth, inclination, base + ground factors (Brinch Hansen 1970 + Vesić 1973 generalizations): qult = c · Nc · sc · dc · ic · gc · bc + q · Nq · sq · dq · iq · gq · bq + 0.5 · γ · B · Nγ · sγ · dγ · iγ · gγ · bγ

Bearing capacity factors (Vesić):

Nq = exp(π · tan φ) · tan²(45° + φ/2)
Nc = (Nq − 1) · cot φ (for φ > 0); Nc = 5.14 for φ = 0
Nγ = 2(Nq + 1) · tan φ

For φ = 30°: Nq = 18.4, Nc = 30.1, Nγ = 22.4. For φ = 35°: Nq = 33.3, Nc = 46.1, Nγ = 48.0. For φ = 40°: Nq = 64.2, Nc = 75.3, Nγ = 109.4.

8.2 Meyerhof 1963

Refined shape + depth + inclination factors. Widely adopted in older textbooks + AASHTO (until 9th ed update).

8.3 Vesić 1973 + Brinch Hansen 1970

Modern AASHTO LRFD uses Vesić formulation. Vesić’s Nγ value is widely accepted as most realistic.

8.4 LRFD bearing-resistance factors

AASHTO LRFD 10.5.5.2.2 — resistance factors φb for shallow foundations:

0.45 sand, semi-empirical (SPT-based).
0.55 sand, rational (CPT-based or laboratory φ’).
0.50 clay (semi-empirical).
0.60 clay (rational, lab Su).
0.45 plate load tests in cohesionless.

IBC 1806 + ASCE 7-22 presumptive bearing values: 3000 psf (144 kPa) sand + gravel, 1500 psf (72 kPa) clay (typical), 12,000 psf (575 kPa) crystalline bedrock.

8.5 Settlement methods

Schmertmann strain-influence — granular soils (§4.4).
Burland + Burbidge — sands, SPT-based; provides settlement at any time.
1D oedometer — saturated clays (Terzaghi consolidation theory §4.1).
Bowles elastic equations — homogeneous half-space; useful for preliminary.
Mat foundations — Winkler subgrade model (modulus of subgrade reaction k) or coupled-spring with structural analysis software (SAFE, RAM Foundation, MAT3D).

8.6 Footing types

Spread (isolated) — single column; square or rectangular.
Combined — two columns when too close for individual footings or near property line.
Strap — eccentric edge footing tied to interior via strap beam.
Continuous wall — strip footing under masonry/concrete wall.
Mat / raft — full-area foundation; high-load buildings on soft soils; high-rise + heavy industrial. Stiffened (downstand beams) or pre-stressed for control of differential settlement.

9. Deep foundations

9.1 Driven piles

H-piles — ASTM A572 Gr 50/65 + A992 steel. HP12×53, HP12×74, HP14×89, HP14×117 common.
Closed-end pipe piles — A252 Gr 2/3. Wall thickness 0.375–1.0 in. Filled with concrete.
Open-end pipe piles — offshore + bridge; develop plug or fully open.
Precast prestressed concrete (PSC) — square 12 + 14 + 16 + 18 + 20 + 24 in; PCI standards. Centrifugally spun cylinder piles (Raymond + Vibro-Concrete).
Timber piles — Douglas fir + southern yellow pine; ASTM D25; below permanent water table only (rot above WT).

Hammers: diesel (Delmag D22 + D30 + D46 + D62, Mitsubishi MH80 + MH120, ICE 80S + 110), hydraulic (Junttan HHK series, IHC S-90 + S-150, APE D-50 + D-80 + D-100), vibratory (ICE 815C + 815L, APE 200 + 400 + 600).

Wave-equation analysis: GRLWEAP (PDI Pile Dynamics, Cleveland OH; founded George Goble 1972 → Frank Rausche). PDA Pile Driving Analyzer + CAPWAP analysis for dynamic load testing.

9.2 Drilled shafts (caissons + bored piles)

Drilled with auger (CFA, continuous-flight auger) or temporary casing + slurry (polymer or bentonite) for hole stability. Diameters typically 600 mm to 3000 mm; depths to 70 m+.

CFA + ACIP (auger-cast-in-place) — continuous auger + concrete pumped through hollow stem during withdrawal. Faster + cheaper than wet construction.
Drilled shaft (drilled pier) — dry or slurry; rebar cage; tremie concrete.
Belled drilled shaft — undercut bell at toe to increase end bearing.

FHWA references: FHWA-NHI-10-016 Drilled Shafts: Construction Procedures + LRFD Design Methods (2010). FHWA-IF-99-025 Micropiles.

9.3 Helical (screw) piles

Square-shaft or pipe-shaft with helical bearing plates welded along the shaft. Torque-installed; capacity correlated to installation torque per ICC-ES AC358 + Hubbell Chance Capacity-to-Torque Ratio Kt. Common diameters 1.5–4 in shaft, 8–14 in helix.

Manufacturers: Hubbell Chance (Centralia MO), MagnumPiering Group (Yorkville IL + acquisitions), EBS Engineered Building Specialties + GoliathTech + IDEAL Foundation Systems.

9.4 Micropiles

Small-diameter (100–300 mm), high-capacity grouted piles installed in drilled holes with structural steel central reinforcement (high-strength bar like Williams + DSI + Dywidag Threadbar). Capacities 50–250 tons. Used for retrofits + tight access + seismic upgrades.

FHWA-SA-97-070 + FHWA-NHI-05-039 Micropile Design + Construction Reference Manual.

9.5 Pile capacity methods

α-method (total stress, clays): fs = α · Su, where α = adhesion factor (Tomlinson 1957; FHWA charts). α = 1.0 for Su < 25 kPa, decreasing to ~0.5 for Su > 100 kPa.

β-method (effective stress, all soils): fs = β · σ’v, where β = K0 · tan δ. β typical 0.25–0.40 for sands, 0.25–0.50 for clays.

λ-method (Vijayvergiya + Focht 1972) — combined α + β; mixed soils.

Nordlund — granular soils + tapered piles.

FHWA / Reese + O’Neill — drilled shafts; α + β with empirical corrections.

End bearing for drilled shafts in cohesionless: qp = Nq · σ’v with Nq cap ~ 60–80; in cohesive: qp = 9 · Su.

9.6 Downdrag (negative skin friction)

Pile through compressing fill or consolidating clay carries downward shear from settling soil. Reduces working capacity. Pile-soil neutral plane analysis (Fellenius 1972 + 1984). Bituminous coating reduces downdrag friction ~ 90 % (Briaud 1995).

9.7 FHWA-HRT-04-043

Reese + O’Neill 1999 + FHWA-HRT-04-043 (2004 update) — drilled shaft side + end resistance correlations widely used in US bridge + building practice.

10. Earth retention

10.1 Cantilever + gravity retaining walls

Lateral earth pressure: Rankine 1857 (active pa, passive pp, smooth wall) — Ka = tan²(45 − φ/2), Kp = tan²(45 + φ/2). Coulomb 1776 — generalizes for wall friction δ + sloped backfill β + battered wall θ.
At-rest K0 — Jaky 1944: K0 = 1 − sin φ’ (NC); K0,OC = K0,NC · OCR^0.5 (Mayne + Kulhawy 1982).
Cantilever: heel + toe + stem. Mat-style for shorter walls (< 6 m). Concrete: ACI 318 Chapter 18 retaining wall provisions.
Counterfort: counterforts (buttresses) every 3–6 m for tall walls.

10.2 Tieback (anchored) walls

Soldier-pile + lagging or sheet-pile wall stabilized by post-tensioned ground anchors. Anchor design: free length + bonded length + grout pressure + creep tests.

PTI DC35.1-14 Recommendations for Prestressed Rock + Soil Anchors. FHWA-IF-99-015 Ground Anchors + Anchored Systems.

Anchor types:

Pressure-grouted — high pressure (> 1 MPa) for sands.
Tube-à-manchette (TAM) — sleeve grouting for staged + multi-tier.
Cone-bottom hole + Williams Form + DSI Strand + Bar Anchors + Stronghold Helical.

10.3 Soldier pile + lagging walls

Driven or drilled HP-pile soldier piles at 6–10 ft (1.8–3.0 m) o.c., timber or shotcrete lagging spans the soldier piles. Mostly temporary cuts; permanent versions exist with concrete face.

10.4 Sheet piles

Hot-rolled steel sections: AZ + PZ + AS + Hoesch Larssen profiles (ArcelorMittal Belval Luxembourg, ThyssenKrupp Hoesch, Voestalpine). Cold-formed lighter sections also available.

AZ 26-700, AZ 36-700N + AZ 48-700N modern high-modulus.
PZ 22 + PZ 27 + PZ 35 + PZ 40 (US — Skyline Steel + Nucor + L.B. Foster).
AS 500-9.5 + AS 500-12.5 + AS 500-12.7 flat sheet pile for cellular cofferdams.

Section modulus + plastic capacity per EN 12063 (driving) + EN 1993-5 (design). API 5L pipe sheet piles for cofferdams.

Installation: impact + vibratory + hydraulic press (silent piling — Giken Silent Piler + ABI Mobilram + Movax SP-100). Vibratory most common; press for noise-sensitive urban + soil-displacement work.

10.5 Secant + tangent pile walls

Cast-in-place drilled secant piles where female (unreinforced) + male (reinforced) piles overlap by 75–150 mm. Used for deep excavations + cutoff walls in urban settings.

Tangent — piles touching, no overlap. Faster but allows seepage between piles.
Hard-soft secant — male reinforced concrete + female cement-bentonite.
Hard-hard secant — male + female both reinforced concrete; full structural wall.

Manufacturers: Bauer BG + RG drilling rigs, Casagrande C series, Soilmec SM/SR series, Liebherr LB + LRB.

10.6 Diaphragm (slurry) walls

Trenched excavation under bentonite or polymer slurry, reinforced cage + tremie concrete. Panel widths 2.4–7.5 m, depths to 100+ m, thicknesses 600–1500 mm.

Equipment: Bauer DHG-V + GB-cutter, Soilmec BH-12 + BH-14 + SC-130, Casagrande KR + KS series.
Bentonite specification: API 13B fluid loss + Marsh viscosity + density.
Synthetic polymer slurries — partial replacement for bentonite; lower environmental burden.

Top-down construction: diaphragm wall installed first; permanent floors cast incrementally as basement excavates downward, providing wall bracing. Used in dense urban sites — One Vanderbilt NYC, Crossrail London + Elizabeth Line stations, Hudson Yards platform.

11. Slope stability

11.1 Infinite slope

For long planar slopes with shallow failure surface parallel to slope: FOS = (c’ + (γ · z · cos²β − γw · zw · cos²β) · tan φ’) / (γ · z · cos β · sin β)

z = depth to failure surface, zw = depth from failure surface to water table, β = slope angle.

For c’ = 0, zw = z (fully saturated): FOS = (γ − γw)/γ · tan φ’ / tan β = γ’ / γsat · tan φ’ / tan β. Saturation + zero cohesion halves stability — explains shallow landslide triggers from rainfall.

11.2 Method of slices — Bishop simplified

Bishop 1955. Vertical slices through circular failure surface. Force equilibrium normal to slice base, moment equilibrium overall. Solves iteratively for FOS:

FOS = (1/Σ Wi·sin αi) · Σ [(c’·b + (Wi − u·b)·tan φ’) / (cos αi · (1 + tan αi · tan φ’ / FOS))]

11.3 Spencer + Morgenstern-Price methods

Spencer 1967 — assumes constant inter-slice force inclination; satisfies both force + moment equilibrium.
Morgenstern-Price 1965 — variable inter-slice force inclination function; more flexible non-circular surfaces.
Janbu Simplified — non-circular surfaces; force-only equilibrium with empirical correction factor.
Janbu Generalized — full force + moment equilibrium.

For routine work, Bishop simplified is preferred for circular surfaces (typically within 5 % of Spencer); Spencer or M-P for non-circular + composite surfaces + back-analysis.

11.4 FOS targets

Long-term static slope: FOS ≥ 1.5.
Dam embankment static end-of-construction: FOS ≥ 1.3.
Rapid drawdown: FOS ≥ 1.2.
Seismic (pseudo-static): FOS ≥ 1.0–1.1.

11.5 Software

Slide2 + Slide3 (Rocscience, Toronto) — industry-standard 2D + 3D limit equilibrium.
GeoStudio SLOPE/W (Bentley/Seequent, Calgary; founded Krahn 1977 GeoSlope Intl) — coupled with SEEP/W, SIGMA/W, QUAKE/W, TEMP/W.
PLAXIS LE (Bentley) — limit equilibrium + FE coupling.
GeoStudio + Slide + SVOFFICE (SoilVision/Bentley) for unsaturated + 3D.

11.6 Probabilistic + reliability

Monte Carlo + Latin Hypercube sampling on c’ + φ’ + γ + groundwater inputs.
Probability of failure Pf typically 1e-3 to 1e-5 target for highway + railway slopes.
JCSS Probabilistic Model Code + EN 1990 Reliability Basis + Phoon + Kulhawy 1999 soil property variability.

12. Seismic geotech

12.1 Liquefaction

Saturated cohesionless soil under cyclic shear loading generates positive pore pressure; if u → σ’v, effective stress → 0 + soil briefly behaves as liquid. Niigata + Anchorage 1964 earthquakes established as significant hazard.

Seed-Idriss simplified procedure (1971, 1985, 1997, 2008 NCEER updates, Idriss + Boulanger 2008 monograph):

Cyclic Stress Ratio CSR = 0.65 · (amax/g) · (σv/σ’v) · rd, where rd = depth-stress reduction.
Cyclic Resistance Ratio CRR from N1,60,cs or qc1Ncs charts.
Factor of safety FS = CRR · MSF · Kσ · Kα / CSR, where MSF = magnitude scaling factor.

Mitigation: vibrocompaction (Keller Vibroflot + Bauer + Soiltec), stone columns + aggregate piers (Geopier Foundation Co.), dynamic compaction (Hayward Baker + Menard Group), deep soil mixing (Raito + Soletanche Bachy + Keller).

12.2 Liquefaction-induced settlement

Ishihara + Yoshimine 1992 + Tokimatsu + Seed 1987. Volumetric strain εv post-liquefaction as function of N1,60 + earthquake-induced shear strain.

12.3 Newmark sliding-block analysis

Newmark 1965. Treats slope or retaining wall as rigid sliding block; cumulative displacement from acceleration time history. Bray + Travasarou 2007 simplified Newmark for embankments. Allowable displacement typical 50–100 mm for highway embankments; < 25 mm for hospitals + lifeline structures.

12.4 Site-specific response (1D site-response analysis)

SHAKE91 / SHAKE2000 — equivalent-linear frequency-domain (Schnabel + Lysmer + Seed 1972).
DEEPSOIL (UIUC, Hashash) — nonlinear time-domain + equivalent-linear.
PSHAKE + ProShake + EERA.
Input: Vs profile + shear-modulus-degradation curves (G/Gmax + damping vs strain — Vucetic + Dobry 1991, Ishibashi + Zhang 1993, Darendeli 2001).

Output: surface response spectrum, peak strains, amplification factors — feeds ASCE 7 site coefficients Fa + Fv.

12.5 Site classification

ASCE 7-22 + NEHRP — Site Classes A (hard rock) through F (soft clay or liquefiable), based on Vs30 (top 30 m time-averaged shear velocity). Class D default Vs30 = 180–360 m/s. Class E < 180 m/s.

13. Ground improvement

Vibrocompaction — cohesionless soils; vibroflot.
Dynamic compaction — drop 10–30 t weight from 10–30 m height.
Stone columns / aggregate piers — Geopier RAP / Impact + Keller VSC.
Deep soil mixing (DSM) + soil-cement columns — Raito CDM, Soletanche Trevimix.
Jet grouting — Trevi Group, Soletanche Bachy.
Compaction grouting + permeation grouting — Hayward Baker + Menard.
Preloading + surcharging + wick drains (PVD prefabricated vertical drains) — Colbond CarboTec, Geotech Drains, MebraDrain.
Lightweight fill — EPS geofoam (BASF Insulfoam, Geofoam Intl); LECA lightweight aggregate; bottom ash.

14. Numerical analysis stack

PLAXIS 2D + 3D (Bentley Systems, Delft origin) — finite-element soil-structure interaction. Hardening Soil + Hardening Soil Small + Soft Soil + Modified Cam Clay + UBCSAND + PM4Sand constitutive models.
FLAC + FLAC3D (Itasca Consulting Group, Minneapolis) — finite-difference; explicit dynamic; large-strain large-deformation. Strong in mining + rock mechanics.
PLAXIS LE / SLIDE2 for limit equilibrium slope stability (§11).
SETTLE3 (Rocscience) — 3D consolidation + settlement.
GEO5 (Fine Software, Prague) — modular geotechnical analysis (eurocode-oriented).
OpenSeesPL + OpenSees — open-source nonlinear FE; performance-based earthquake engineering.
Abaqus + LS-DYNA — general FE; specialist soil-structure-interaction + impact + blast.
GeoStudio suite — SEEP/W, SLOPE/W, SIGMA/W, QUAKE/W, TEMP/W, CTRAN/W, AIR/W, VADOSE/W.

15. Notable case histories

Leaning Tower of Pisa — 1173 construction begin, lean discovered immediately due to settlement on Pliocene clay. 1990–2001 stabilization (Burland + Polvani et al.) via soil extraction + counterweights reduced lean from 5.5° to ~3.97°. Stable to ~2200.
Mexico City — pumping of aquifer caused regional subsidence + differential settlement of historic structures. Metropolitan Cathedral (1573 build) underpinned 1989–1998 with 1500 m³ jet grouting + selective surcharging.
Transcona Grain Elevator Failure 1913 (Manitoba) — bearing-capacity failure into soft clay; classic textbook example.
Teton Dam failure 1976 (Idaho) — internal erosion of fill at right abutment key trench; 11 dead, 11k displaced; FERC + Bureau of Reclamation overhaul.
Lower Lake Hodges 2010 + Oroville Spillway 2017 — emergency-spillway erosion + foundation issues.
Singapore Nicoll Highway collapse 2004 — diaphragm-wall strutting failure during MRT excavation, 4 fatalities. Triggered Singapore BCA + LTA review of deep-excavation practice.
Big Dig CA/T project Boston 1991–2007 — extensive ground freezing + slurry-walls + jet-grouting in soft Boston Blue Clay.

Compendium

Explorer

Geotechnical Engineering — Soil, Foundations, Earth Retention, Slopes, Seismic