Soil Mechanics & Geotechnical Engineering — Engineering Reference

1. At a glance

Soil mechanics is the branch of engineering mechanics that treats soil — a three-phase particulate medium of mineral solids, water, and air — as the structural material that supports almost every constructed work on earth. Geotechnical engineering is its applied wing: foundations (shallow and deep), retaining walls, slope stability, embankments, earth and tailings dams, tunnels, pavements, ground improvement, and soil-structure interaction under static and seismic load.

Unlike steel or concrete, soil is heterogeneous, anisotropic, history-dependent, partially saturated, time-dependent, and rarely directly observable below 1-2 m depth. Its behaviour is governed not by the stress on the bulk medium but by effective stress σ’ = σ - u, the part carried skeleton-to-skeleton between grains, after pore-water pressure u is subtracted (Terzaghi 1925). Every quantitative move in the discipline — bearing capacity, settlement, slope FS, retaining-wall earth pressure, liquefaction trigger — flows from this single decomposition.

The discipline sits where the design stack meets the unknown: site investigation produces samples and N-values, not a CAD model. Laboratory and in-situ testing, empirical correlation, analytical closed-form solutions, finite-element / finite-difference simulation, and engineering judgement combine in roughly equal parts. Foundation failures are reminders the discipline is not solved: Leaning Tower of Pisa (started 1173, 5.5° lean by 1990 from differential consolidation of soft clay), Teton Dam 1976 (internal erosion in fissured loess, 11 dead), Mexico City subsidence (10+ m settlement of lakebed clay over a century), Transcona Grain Elevator 1913 (classic bearing-capacity failure on Winnipeg clay), Rissa landslide 1978 (Norwegian quick-clay flow slide), Brumadinho 2019 (upstream tailings-dam liquefaction, 270 dead), Champlain Towers South 2021 (long-term degradation with debated soil-corrosion contribution, 98 dead).

Place in the design stack: site investigation → soil classification + parameters → analytical/FE analysis → foundation/wall/slope design → construction observation → instrumentation/monitoring.

2. Why it matters

Every structure rests on soil or rock, and the foundation is usually the second-most-costly subsystem of a building (after the superstructure) and the most expensive subsystem of a bridge, dam, port, or industrial facility. Soil failure causes building collapse, landslides, levee and dam breaches, pipeline rupture, and pavement loss. The cost of inadequate geotechnical investigation is famously asymmetric: 0.5-1 % of project cost spent up front avoids 5-30 % cost overruns and weeks-to-months of schedule loss when an unexpected soft layer, perched water table, expansive clay, or buried debris is discovered during excavation. The geotechnical engineer is liable: foundation-related litigation accounts for a disproportionate share of professional-liability claims in civil engineering, and many jurisdictions (California, Florida) require licensed geotechnical sign-off on every habitable structure.

Compared with steel and concrete, soil parameters carry typical coefficient-of-variation 0.2-0.6, an order of magnitude wider than σ_y on a steel coupon. The factor-of-safety values quoted below (FS = 3 on bearing capacity, FS = 1.5 on slopes) are calibrated to those uncertainties; load-and-resistance-factor design (LRFD, AASHTO LRFD Bridge Design Specifications, EN 1997-1 Eurocode 7) is gradually replacing the global-FS approach but the same total margin of safety is preserved.

3. First principles

3.1 Phase relationships

Soil is a three-phase medium: solid grains, water, air. Volume and mass relationships:

V_t = V_s + V_v   ;   V_v = V_w + V_a            (volumes)
M_t = M_s + M_w                                   (masses; M_air ≈ 0)
n  = V_v / V_t           (porosity, 0 < n < 1)
e  = V_v / V_s           (void ratio, 0 < e < ∞)  ;  n = e / (1 + e)
w  = M_w / M_s           (water content, % of dry mass)
S  = V_w / V_v           (degree of saturation, 0 - 1)
γ  = M_t · g / V_t       (total unit weight)
γ_d = M_s · g / V_t      (dry unit weight)
γ_s = G_s · γ_w          (solid-particle unit weight)
γ' = γ_sat − γ_w         (buoyant / submerged unit weight)

with γ_w = 9.81 kN/m³ (62.4 pcf) and specific gravity G_s ≈ 2.65-2.70 for quartz sands, 2.70-2.80 for clay minerals (kaolinite, illite), 2.90-3.00 for iron-rich or heavy-mineral soils. Two useful identities: S·e = w·G_s (Lambe-Whitman) and γ_d = γ / (1 + w).

3.2 Atterberg limits (Casagrande 1932, 1948)

For fine-grained soils, water content controls consistency. The Atterberg limits (Atterberg 1911) mark transition water contents between four states: solid → semi-solid → plastic → liquid.

Limit	Symbol	Method (ASTM D4318)
Shrinkage limit	SL	Volume change ceases as soil dries
Plastic limit	PL	Soil crumbles when rolled to 3.2 mm thread
Liquid limit	LL	25-blow Casagrande cup closure (or fall-cone equivalent BS 1377)

Plasticity index PI = LL - PL. Liquidity index LI = (w - PL) / PI distinguishes brittle (LI < 0) from sensitive (LI > 1, where natural water content exceeds LL — characteristic of Norwegian quick clay and Champlain Sea clay).

3.3 USCS classification (ASTM D2487)

The Unified Soil Classification System assigns a two-letter group symbol from grain-size distribution and Atterberg limits:

Group	Primary	Modifier	Description
GW	Gravel	Well-graded	Cu ≥ 4, 1 ≤ Cc ≤ 3, <5 % fines
GP	Gravel	Poorly graded	Fails GW gradation
GM	Gravel	Silty	>12 % fines, PI < 4
GC	Gravel	Clayey	>12 % fines, PI > 7
SW, SP, SM, SC	Sand	Same modifiers	Sand fraction (>50 % retained on #200)
CL	Clay	Low plasticity	LL < 50, plots above A-line
CH	Clay	High plasticity	LL ≥ 50, plots above A-line
ML	Silt	Low plasticity	LL < 50, plots below A-line
MH	Silt	High plasticity	LL ≥ 50, plots below A-line
OL/OH	Organic	Low/high plasticity	LL ratio (oven-dry/natural) < 0.75
PT	Peat	—	Highly organic, fibrous

A-line: PI = 0.73·(LL - 20). Clays plot above; silts and organics plot below. The chart is the canonical fines-discriminator and appears on every USCS report (Casagrande’s plasticity chart, 1948).

3.4 Effective stress (Terzaghi 1923, 1925)

The defining concept of modern soil mechanics. At any depth in a saturated soil, the total stress σ on a horizontal plane equals the weight of overlying material per unit area; the pore-water pressure u acts equally in all directions in the water phase; what remains is carried by the soil skeleton:

σ' = σ − u                       (effective stress)

All strength, stiffness, and volume-change behaviour is controlled by σ’, not σ. Raising u (e.g. by rainfall infiltration, rapid drawdown, or earthquake pore-pressure buildup) reduces σ’ without changing σ, and can trigger failure — the mechanism behind slope failures after heavy rain, dam piping, and soil liquefaction.

3.5 Shear strength — Mohr-Coulomb (Coulomb 1776, Mohr 1900)

On any plane through the soil, shear failure occurs when shear stress τ on that plane reaches:

τ_f = c' + σ'_n · tan(φ')           (effective-stress, drained)
τ_f = s_u                            (total-stress, undrained, φ = 0)

where c’ = effective cohesion, φ’ = effective friction angle, s_u = undrained shear strength (also c_u).

Soil	c’ (kPa)	φ’ (°)	s_u (kPa)
Loose sand	0	28-32	(drained)
Medium-dense sand	0	32-36	(drained)
Dense sand	0	36-42	(drained)
Gravel	0	36-45	(drained)
NC clay, soft	0-5	18-25	12-25
NC clay, medium	0-10	22-28	25-50
OC clay, stiff	10-30	25-30	50-100
OC clay, hard	20-100	28-35	100-200+
Residual (post-failure)	0	8-15 (residual φ’_r)	(Skempton 1985)

Cohesionless soils (sands, gravels) have c’ ≈ 0 and strength is purely frictional. Cohesive soils (clays) develop apparent cohesion from particle bonding and capillary suction. Critical-state friction angle φ’_cv is reached at large strain regardless of initial density (Roscoe-Schofield-Wroth 1958, Critical State Soil Mechanics 1968).

3.6 Compaction (Proctor 1933)

Engineered fills are placed and compacted in lifts to a target density. The standard Proctor test (ASTM D698) and modified Proctor test (ASTM D1557) plot dry unit weight γ_d vs. moulding water content w; the curve peaks at the optimum water content w_opt and the maximum dry density γ_d,max. Field compaction is then specified as a percentage of γ_d,max (typically 95 % standard or 92-95 % modified for structural fill, 90 % for landscape) within ±2 % of w_opt.

Test	Hammer mass	Drop	Layers	Blows/layer	Compactive energy
Standard Proctor (ASTM D698)	2.5 kg	305 mm	3	25	600 kN·m/m³
Modified Proctor (ASTM D1557)	4.54 kg	457 mm	5	25	2700 kN·m/m³

Field compaction methods: smooth-drum / vibratory rollers (cohesionless), sheepsfoot / pad-foot rollers (cohesive), impact rollers (deep dynamic compaction of loose sand to 6-10 m), heavy tampers (dynamic consolidation, Menard 1970s, to 30 m), vibroflotation / vibro-replacement (stone columns). Quality control by nuclear density gauge (ASTM D6938), sand-cone (D1556), drive-cylinder, or rapid-impact compactor pass count.

3.7 Consolidation (Terzaghi 1923, 1943)

Saturated clay loaded by a new surcharge cannot deform immediately — water must drain through the low-permeability fabric. The time-dependent settlement is consolidation, governed by the one-dimensional diffusion equation:

∂u / ∂t = c_v · ∂²u / ∂z²            (Terzaghi 1D consolidation)
c_v = k · M / γ_w  =  k · (1 + e₀) / (a_v · γ_w)
T_v = c_v · t / H_d²                 (time factor; H_d = drainage path)
U   = degree of consolidation = f(T_v)

with c_v = coefficient of consolidation (m²/s), k = hydraulic conductivity (m/s), M = constrained modulus from oedometer, a_v = coefficient of compressibility, H_d = maximum drainage path (half the layer thickness if drained both sides, full thickness if drained one side).

Key U vs T_v values (Terzaghi’s solution, Fourier series):

U (%)	T_v
10	0.008
30	0.071
50	0.197
60	0.286
70	0.403
80	0.567
90	0.848
95	1.129
99	1.781

Approximate formulas: T_v = (π/4)·U² for U ≤ 60 %; T_v = 1.781 - 0.933·log(100 - U%) for U > 60 %.

The drainage path H_d is the longest distance a water particle must travel to a free-draining boundary: H_d = full layer thickness for single drainage (one permeable + one impermeable boundary), H_d = half thickness for double drainage. Halving H_d (e.g. by installing vertical wick drains, prefabricated vertical drains / PVDs at 1-2 m grid) reduces consolidation time by a factor of four — the foundation of preload + PVD ground improvement for soft clay sites (highway embankments on Boston blue clay, Bangkok marine clay, Champlain Sea clay).

Magnitude of primary consolidation settlement of a clay layer of initial thickness H₀ and void ratio e₀ under stress increase Δσ’:

s_c = H₀ · C_c / (1 + e₀) · log(σ'_f / σ'_0)        (NC clay)
s_c = H₀ · C_s / (1 + e₀) · log(σ'_f / σ'_0)        (OC clay below σ'_p)

with C_c = compression index (slope of e-log σ’ curve on virgin compression), C_s = swelling/recompression index, σ’_p = preconsolidation pressure. Typical C_c = 0.009·(LL - 10) (Skempton 1944 empirical). Secondary compression (creep) follows at log-linear rate C_α over the log of time after primary consolidation completes; C_α / C_c ≈ 0.04 ± 0.01 for inorganic clays (Mesri-Godlewski 1977), rising to 0.05-0.07 for organic clay and 0.05-0.10 for peat.

3.8 Permeability and seepage (Darcy 1856)

Flow of water through saturated soil obeys Darcy’s law:

v = k · i               (Darcy flux; v = Q/A apparent velocity)
i = Δh / L              (hydraulic gradient)
Q = k · i · A           (volumetric flow rate)

with hydraulic conductivity (or coefficient of permeability) k spanning fourteen orders of magnitude across natural soils — the widest range of any engineering parameter:

Soil	k (m/s)
Gravel	10⁻¹ to 10⁻³
Clean sand	10⁻³ to 10⁻⁵
Silty sand	10⁻⁵ to 10⁻⁷
Silt	10⁻⁷ to 10⁻⁹
Clay	10⁻⁹ to 10⁻¹²
Compacted clay liner	10⁻¹⁰ to 10⁻¹¹ (regulatory min for landfill: 1×10⁻⁹)

Field tests: falling-head / constant-head permeameter (lab, ASTM D5084), pumping test (aquifer-scale, multi-well), slug test (Bouwer-Rice 1976, Hvorslev 1951), packer test (rock, USBR 1974), piezocone dissipation test (CPTu).

Flow nets (Forchheimer 1898, Casagrande 1937) graphically solve 2-D steady seepage as orthogonal flow lines and equipotentials; modern practice uses FE software (SEEP/W, PLAXIS Flow, FEFLOW). Critical for dam seepage, excavation dewatering, levee stability, groundwater contamination transport.

Critical hydraulic gradient (quicksand / heave at base of cofferdam): i_c = γ’ / γ_w ≈ 1.0 for typical sand. Boiling occurs when upward i ≥ i_c; design with FS ≥ 1.5-2.0 against heave.

3.9 Constitutive models in geotechnical FE

Model	Parameters	Captures	Limitations
Linear elastic	E, ν	Pre-yield response only	No plasticity, unrealistic at large strain
Mohr-Coulomb (MC)	E, ν, c’, φ’, ψ (dilation)	Shear strength, perfect plasticity	Constant E with depth, no stiffness degradation
Hardening Soil (HS, Schanz-Vermeer-Bonnier 1999)	E₅₀, E_oed, E_ur, m, c’, φ’, ψ	Stress-dependent stiffness, double-yield	Calibration effort
HS-small (Benz 2007)	+ G₀, γ₀.₇	Small-strain stiffness (excavations)	More parameters
Modified Cam-Clay (Roscoe-Burland 1968)	λ, κ, M, e_cs, ν	Critical-state, OC/NC clay, hardening	Sands less well represented
Hypoplasticity (Kolymbas, von Wolffersdorff 1996)	8 + parameters	Rate-form, no yield surface	Granular only; complex calibration
UBCSAND, PM4Sand (Beaty-Byrne 2011, Boulanger-Ziotopoulou 2017)	~10 parameters	Cyclic, liquefaction	Earthquake-engineering only

Selection rule of thumb: MC for screening (slope stability, simple bearing capacity), HS / HS-small for staged excavations and settlement (urban geotech), Cam-Clay for soft clay consolidation, PM4Sand / UBCSAND for seismic liquefaction analysis.

4. In-situ testing

Disturbance during sampling biases laboratory tests, especially for sensitive clays and loose sands. In-situ tests measure soil response in place.

Test	Standard	Measures	Best for	Output
SPT (Standard Penetration Test)	ASTM D1586	Blows per 12” with split-spoon driven by 63.5 kg hammer at 76 cm drop	Granular soils, routine investigation	N-value → φ’, D_r
CPT / CPTu (Cone Penetration Test)	ASTM D3441 / D5778	Continuous tip resistance q_c, sleeve friction f_s, pore pressure u₂	All soils, soft to medium	Soil behaviour type chart (Robertson 1990)
DMT (Marchetti Dilatometer)	ASTM D6635	Blade lift-off and 1.1 mm displacement pressures	Most soils, especially clays	K_D, I_D, E_D
PMT (Pressuremeter, Ménard or self-boring)	ASTM D4719	Cavity expansion pressure-volume curve	All soils, rock	E_PMT, p_lim
FVT (Field Vane)	ASTM D2573	Torque to rotate cruciform vane	Soft clay s_u	s_u, sensitivity S_t = s_u,peak / s_u,remoulded
Seismic CPT / Crosshole / Downhole	ASTM D7400 etc.	Shear-wave velocity V_s	Site-response, V_S30	V_s profile → G_max = ρ·V_s²
MASW (Multichannel Analysis of Surface Waves)	—	Surface-wave dispersion → V_s	Non-invasive site characterization	V_s profile
Boring + Shelby tube	ASTM D1587	Undisturbed clay sample	Laboratory triaxial / oedometer	Lab parameters

Correlations (SPT, sand):

• (N₁)₆₀ corrected for overburden + hammer energy: φ’ ≈ 27.5 + 9.2·log(N₁)₆₀ (Hatanaka-Uchida 1996)
• Relative density: D_r (%) ≈ 21·√[(N₁)₆₀ / (σ’_v / p_a + 0.7)] (Skempton 1986)

Correlations (SPT, clay): s_u (kPa) ≈ 4-6·N (rough, only for screening — always confirm with UU or vane).

CPT soil behaviour type (Robertson 1990, 2010): plot normalized tip Q_t vs normalized friction F_r and pore-pressure ratio B_q; nine zones map to USCS-like classes with continuous profiling.

5. Soil types and behaviour

• Gravel + Sand (cohesionless). Drainage is fast, c’ ≈ 0, strength from interlocking and friction. Bearing capacity governed by φ’, settlement is essentially immediate (elastic). Liquefies if saturated and loose during earthquake (§9).

• Silt (non-plastic to low-plastic). Intermediate permeability, sensitive to disturbance, susceptible to frost heave. Dilatant (volume increase under shear) when dense, contractive when loose.

• Clay (cohesive).

  • Normally consolidated (NC): never previously at higher load; σ’_p ≈ current σ’_v.
  • Overconsolidated (OC): previously consolidated to σ’_p higher than current σ’_v (glacial loading, erosion of overburden, desiccation); stiffer at small strain, peaks above critical state, then softens to residual.
  • Sensitive / quick clay (Norwegian + Champlain Sea clays): marine clays whose flocculated structure collapses to slurry on disturbance — S_t > 30; Rissa 1978 is the textbook flow slide.

• Peat / organic soil. Extremely compressible (C_c > 1), very low strength, large secondary compression. Ground improvement (preload + wick drains, deep mixing, replacement) almost always required for foundation support.

• Loess. Wind-deposited silt with metastable open structure cemented by carbonates or clay bridges; collapses on wetting under load — Mississippi-valley loess, Chinese yellow earth, Iowa till-line loess. Teton Dam (1976) failed in fissured loess.

• Expansive clay (smectite, bentonite, montmorillonite). Shrink/swell of 5-30 % with seasonal moisture change. Foundation damage common in Texas Gulf Coast, Colorado Front Range, Denver basin, India’s black-cotton soils, central Spain. Mitigation: deep foundations below active zone, moisture-controlled subgrade, post-tensioned slabs, lime/cement stabilization.

• Frozen soil / permafrost. Ice acts as cementing agent; thaw → catastrophic settlement and loss of bearing. Arctic and Antarctic engineering, Trans-Alaska pipeline design.

• Saturated cohesionless soil under cyclic load. Liquefaction risk during earthquake — pore pressure builds, σ’ → 0, sand loses strength (§9).

6. Foundation design

6.1 Shallow foundations

Used when competent soil is within 1-3 m of grade.

Spread / strip footings: square, rectangular, or continuous (under wall).

Mat / raft foundation: continuous slab carrying the entire structure; used when individual footings would overlap (>60 % footprint), or to bridge over weak/variable subgrade, or to provide buoyancy.

Bearing capacity — Terzaghi 1943 / Meyerhof 1963 (general bearing-capacity equation):

q_ult = c'·N_c·s_c·d_c·i_c + γ·D_f·N_q·s_q·d_q·i_q + 0.5·γ·B·N_γ·s_γ·d_γ·i_γ

• N_c, N_q, N_γ: bearing-capacity factors, functions of φ’ only
• s_, d_, i_*: shape, depth, load-inclination correction factors
• B: footing width; D_f: embedment depth; γ: soil unit weight (use γ’ below water table)

φ’ (°)	N_c	N_q	N_γ (Meyerhof)
0	5.14	1.0	0
5	6.49	1.57	0.45
10	8.35	2.47	1.22
15	10.98	3.94	2.65
20	14.83	6.40	5.39
25	20.72	10.66	10.88
30	30.14	18.40	22.40
35	46.12	33.30	48.03
40	75.31	64.20	109.4
45	133.87	134.87	271.7

For purely cohesive soil (φ = 0): q_ult = 5.14·s_u·s_c·d_c (Skempton 1951 form). For long strip footings, s_c, s_γ = 1.

Allowable bearing pressure: q_allow = q_ult / FS, with FS = 3 typical for static, 2 for seismic / wind extreme.

Settlement:

• Immediate (elastic): s_i = q·B·(1 - ν²)·I_w / E_s (Boussinesq-based; sand)
• Consolidation: equation in §3.6 (clay)
• Tolerable angular distortion: δ/L < 1/500 (most structures), 1/1000 (sensitive cladding, machinery) — Skempton-MacDonald 1956, Polshin-Tokar 1957, Bjerrum 1963 chart.

6.2 Deep foundations

Used when shallow competent soil is absent, or loads are large, or uplift/lateral capacity is required.

Type	Diameter	Capacity range	Typical use
Timber pile	200-400 mm	100-400 kN	Light residential, marine, historical
Driven steel H-pile (HP10-HP14)	250-360 mm	500-2500 kN	Bridges, buildings on bedrock
Driven pipe pile (open/closed end)	250-1500 mm	500-5000 kN	Marine, deep waterfront
Prestressed precast concrete pile	300-900 mm	500-3000 kN	Buildings, bridges
Drilled shaft / caisson	600-3000 mm	1000-20000 kN	Heavy bridges, tall buildings
Auger-cast (CFA)	300-900 mm	500-3000 kN	Urban (low noise/vibration)
Micropile	100-300 mm	200-1000 kN	Underpinning, restricted access
Helical pile	75-350 mm shaft + plates	50-500 kN	Solar racks, light frames, repair

Pile capacity = end-bearing + skin friction:

Q_ult = Q_p + Q_s = q_p · A_p + Σ f_s,i · A_s,i

End-bearing (sand): q_p = N_q · σ’_v (effective overburden at tip), capped at empirical limits (Meyerhof 1976, ~ q_p,max = 0.5·N_q·tan φ’ MPa). Skin friction (sand): f_s = K_s · σ’_v · tan δ, with K_s ≈ 0.7-1.0·K_0 (driven), δ ≈ 0.75-1.0·φ’ (steel against sand). Skin friction (clay) — α method: f_s = α · s_u, with α from API RP 2GEO chart (1.0 for soft clay, dropping to 0.3-0.5 for stiff). Skin friction (clay) — β method: f_s = β · σ’_v, with β = K·tan φ’ typically 0.2-0.4 (NC clay).

Verification tests: ASTM D1143 static axial load test (definitive; 200 % design load + creep), ASTM D4945 high-strain dynamic testing (PDA + CAPWAP), ASTM D7383 statnamic, ASTM D8169 bidirectional (Osterberg cell).

Lateral pile capacity is a separate problem governed by soil-structure interaction. The p-y method (Reese-Matlock 1956, Matlock 1970 for soft clay, Reese-Cox-Koop 1974 for sand, API RP 2GEO for offshore) models the pile as a beam-on-nonlinear-Winkler-foundation, with springs p (force per length) vs deflection y from empirical p-y curves. Software: LPILE (Ensoft), PLAXIS 2D Embedded Pile Row, FB-MultiPier (FDOT). Group effects reduce capacity per pile by 0.4-0.8 (p-multiplier) depending on spacing s/D.

Negative skin friction (down-drag) occurs when surrounding soil settles more than the pile (consolidating clay under fill load, lowered groundwater) — the soil drags the pile downward, adding axial load. Mitigated with bitumen coating on the affected length.

6.3 Retaining walls

Earth-pressure theories:

• Rankine 1857: active K_a = tan²(45° - φ’/2), passive K_p = tan²(45° + φ’/2); assumes vertical smooth wall, horizontal backfill.
• Coulomb 1776: wedge equilibrium with wall friction δ and sloping back face; K_a + K_p in closed form for cohesionless backfill.
• At-rest: K_0 = 1 - sin φ’ (Jaky 1944) for NC; K_0 = (1 - sin φ’)·(OCR)^(sin φ’) for OC.

Active pressure mobilizes at wall-top displacement Δ ≈ 0.001-0.004·H; passive needs 10× more.

Wall types:

• Gravity / cantilever RC: moment + sliding + overturning checks, FS_sliding ≥ 1.5, FS_overturning ≥ 2.0.
• Sheet pile: steel U or Z section; cantilever (H ≤ 4-5 m) or anchored (deeper).
• Soldier-pile and lagging: soldier piles driven, timber/concrete lagging between; temporary excavation support.
• Secant / tangent pile wall: overlapping bored piles, waterproof.
• Diaphragm (slurry) wall: concreted in bentonite slurry trench; deep urban excavation, top-down construction.
• MSE (Mechanically Stabilized Earth): geosynthetic / metal-strip reinforced fill behind precast facing panels; highways, abutments.
• Soil nail + shotcrete: drilled/grouted bars + shotcrete face; open-cut stabilization in cohesive or cemented soil.

6.4 Ground improvement

When in-situ soil is inadequate, modify it rather than over-design the foundation.

Technique	Target soil	Effect	Typical depth
Surcharge preload + PVD	Soft clay, peat	Pre-consolidate, gain strength	3-30 m
Vibro-compaction	Loose clean sand (FC < 15 %)	Densify, increase φ’, D_r	5-25 m
Vibro-replacement (stone columns)	Soft clay, silty sand	Composite stiffness + drainage	5-20 m
Dynamic compaction (Menard)	Loose sand, granular fill	Densify by impact	5-10 m (heavy tamper to 30 m)
Deep soil mixing (DSM)	Soft clay, organic	Cement/lime-soil columns or panels	5-40 m
Jet grouting	All except gravels	Soilcrete columns, water cutoff	5-50 m
Compaction grouting	Loose granular	Densify by displacement	Variable
Permeation grouting	Coarse sand, gravel	Fill voids, water cutoff	Variable
Chemical / lime stabilization	Expansive clay, subgrade	Reduce PI, increase strength	Surficial (subgrade)
Geosynthetic reinforcement	Embankment fill	Tensile capacity, basal stability	Surface to ~3 m
Electro-osmosis (Casagrande 1939)	Silt, soft clay	Dewater, consolidate	Specialty
Freezing (artificial ground freezing)	Saturated soil	Temporary impermeable strength	5-30 m

7. Worked examples

Example A — Strip footing on sand (Terzaghi/Meyerhof)

Problem. A 1.5 m wide continuous footing, embedded D_f = 1.0 m, on dry medium-dense sand with γ = 18 kN/m³ (115 pcf), φ’ = 35°, c’ = 0. Find q_allow with FS = 3.

Step 1 — Pick N factors. From the table at φ’ = 35°: N_c = 46.12, N_q = 33.30, N_γ = 48.03 (Meyerhof).

Step 2 — Strip footing shape factors = 1. (Continuous strip; s_c = s_q = s_γ = 1.0. Depth factors d ≈ 1.0 for shallow D/B = 0.67. Ignore inclination.)

Step 3 — Bearing capacity.

q_ult = c'·N_c + γ·D_f·N_q + 0.5·γ·B·N_γ
      = 0 + 18·1.0·33.30 + 0.5·18·1.5·48.03
      = 0 + 599.4 + 648.4
      = 1247.8 kPa  (~26 ksf)

Step 4 — Allowable. q_allow = 1247.8 / 3 = 416 kPa (~ 8.7 ksf).

Step 5 — Net allowable. Subtract D_f·γ = 18 kPa (the soil that was excavated): q_allow,net ≈ 398 kPa (~ 8.3 ksf). The footing can carry P/L ≈ 398·1.5 ≈ 597 kN/m run of footing (~ 41 kip/ft).

Comment. Settlement, not bearing capacity, usually governs spread-footing design on sand. Check elastic settlement against 25 mm (1 in) total / 19 mm (0.75 in) differential per Skempton-MacDonald.

Example B — Driven H-pile in sand

Problem. A 12 m long HP12×74 (steel H-pile, perimeter ≈ 1.20 m, area A_p ≈ 0.014 m² steel × box-area 0.060 m² with soil plug) driven in medium-dense sand: γ = 18 kN/m³, φ’ = 33°, water table at depth. Estimate Q_ult and Q_allow with FS = 2.

Step 1 — Mean effective vertical stress along shaft. σ’_v,avg = γ · 6 m = 108 kPa (mid-depth).

Step 2 — Skin friction. Take K_s · tan δ ≈ 0.4 (driven steel pile, NavFac DM-7).

f_s,avg = 0.4 · 108 = 43.2 kPa
Q_s = f_s,avg · perimeter · length = 43.2 · 1.20 · 12 = 622 kN

Step 3 — End-bearing. At tip σ’_v = 18·12 = 216 kPa. N_q (Meyerhof, driven pile in sand) ≈ 60 at φ’ = 33° (pile bearing-capacity factor, larger than footing N_q because of confinement).

q_p = 60 · 216 = 12 960 kPa, cap at ~ 10 000 kPa
Q_p = q_p · A_p,plugged = 10 000 · 0.060 = 600 kN

Step 4 — Ultimate and allowable.

Q_ult = Q_s + Q_p = 622 + 600 = 1222 kN  (~ 275 kip)
Q_allow = Q_ult / 2 = 611 kN  (~ 137 kip)

Comment. Proof-test at minimum 200 % design load (ASTM D1143) or high-strain PDA (ASTM D4945) for the production piles. The static formula alone has ± 30 % typical accuracy.

Example C — Infinite-slope stability (cohesionless)

Problem. A long uniform sand slope at β = 30°, φ’ = 35°, c’ = 0. Check FS dry and fully saturated (water table at surface).

Step 1 — Dry case.

FS = tan φ' / tan β = tan 35° / tan 30° = 0.7002 / 0.5774 = 1.21    ✓ stable

Step 2 — Saturated, seepage parallel to slope. Effective unit weight γ’ = γ_sat - γ_w. Take γ_sat = 20 kN/m³, γ_w = 9.81 kN/m³, so γ’/γ_sat = 10.19 / 20 = 0.510.

FS = (γ'/γ_sat) · (tan φ' / tan β) = 0.510 · 1.21 = 0.62    × failure

Step 3 — Implication. Even a moderate sand slope that is stable dry fails when fully saturated with seepage parallel to the slope. This is why every natural and engineered slope must be drained — perimeter and chimney drains, weep holes, slope-toe blanket drains, horizontal drainage borings (HDBs). It is also why “the slope held for 50 years” is not evidence — it held in the dry / partially saturated state. The first 100-year storm changes the boundary condition.

Example D — Cantilever retaining wall, Rankine active

Problem. A 4.0 m high cantilever RC retaining wall, vertical back face, horizontal granular backfill γ = 19 kN/m³ (121 pcf), φ’ = 32°, c’ = 0, no surcharge, no water table. Wall stem + base weighs W = 95 kN/m run, with centroid 1.4 m back from the toe; base is 2.4 m wide; base friction tan δ_b = 0.55.

Step 1 — Active earth-pressure coefficient.

K_a = tan²(45° − φ'/2) = tan²(45° − 16°) = tan²(29°) = 0.307

Step 2 — Active thrust (triangular distribution).

P_a = 0.5 · K_a · γ · H² = 0.5 · 0.307 · 19 · 4.0² = 46.7 kN/m
     applied at H/3 = 1.33 m above the base, horizontal.

Step 3 — Overturning about the toe.

M_OT = P_a · H/3 = 46.7 · 1.33 = 62.1 kN·m/m
M_R  = W · arm  = 95 · 1.4    = 133  kN·m/m
FS_OT = M_R / M_OT = 2.14    ✓  (≥ 2.0)

Step 4 — Sliding.

H_drive  = P_a            = 46.7 kN/m
H_resist = W · tan δ_b    = 95 · 0.55 = 52.3 kN/m
FS_sliding = 52.3 / 46.7  = 1.12   × (< 1.5)

Sliding governs and the check fails. Standard fixes: lengthen the heel (mobilize more backfill weight on the base), add a base shear key projecting 0.5-1 m into competent soil to mobilize passive resistance, increase base roughness with a roughened concrete pour, or add a granular drain + passive wedge ahead of the toe. A 0.5 m shear key contributes K_p · γ · d² / 2 ≈ 3.25 · 19 · 0.25 / 2 ≈ 7.7 kN/m of additional passive resistance, taking FS_sliding to ~1.30 — still short of 1.5, demonstrating that retaining-wall design routinely iterates 3-4 cycles on base geometry.

8. Slope stability

8.1 Methods

Limit-equilibrium methods assume a slip surface, compute resisting and driving forces/moments, define FS = resisting / driving. Differences in how they treat inter-slice forces and force/moment equilibrium:

Method	Slip surface	Inter-slice forces	Equilibrium	Notes
Fellenius / Swedish	Circular	None (Σ = 0)	Moment only	Oldest; conservative for low FS
Bishop simplified (1955)	Circular	Horizontal only	Moment only	Industry standard, easy to converge
Janbu simplified (1957)	Non-circular	Horizontal	Force only	With correction factor f_0
Janbu generalized	Non-circular	Both	Both	Iterative, slow
Spencer (1967)	Any	Constant inclination	Both	Rigorous, widely used
Morgenstern-Price (1965)	Any	Variable inclination function f(x)	Both	Most rigorous LEM
Sarma (1973)	Any	Vertical interfaces	Both	Critical horizontal acceleration

Finite-element / finite-difference strength-reduction (SRM): progressively reduce c’/SRF, tan φ’/SRF until convergence fails; SRF at failure ≈ FS. PLAXIS, FLAC, RS2 all implement this. SRM doesn’t require pre-defining the slip surface.

8.2 Slip-surface geometry

Soil	Typical surface
Homogeneous clay	Circular (toe, base, slope)
Stratified soil with weak seam	Compound (block + log spiral)
Cohesionless soil	Planar (infinite slope)
Rock with discontinuities	Planar / wedge / toppling (Markland test)
Soft over stiff	Base-circle through soft layer

8.3 FS targets

Condition	FS minimum
Permanent slope, long-term, dam	1.5
Permanent slope, drained, building	1.3-1.5
Temporary excavation (months)	1.2-1.3
End-of-construction (undrained)	1.3
Rapid drawdown (dam)	1.1-1.3
Seismic (pseudo-static k_h = 0.1-0.2 g)	1.0-1.1

Pseudo-static seismic analysis uses a horizontal coefficient k_h applied to slice weight to model earthquake force. Newmark sliding-block (1965) gives displacement given an acceleration time history and a yield acceleration — preferable to pseudo-static for design under modern codes.

9. Seismic geotechnical

9.1 Site classification (ASCE 7-22 Ch. 20)

Site Class	V_S30 (m/s)	N̄ (SPT)	s̄_u (kPa)	Description
A	> 1500	—	—	Hard rock
B	760-1500	—	—	Rock
BC	555-760	—	—	(new in ASCE 7-22)
C	365-760	> 50	> 95	Dense soil / soft rock
CD	270-365	—	—	(new in ASCE 7-22)
D	180-365	15-50	47-95	Stiff soil (default if data lacking)
DE	150-180	—	—	(new in ASCE 7-22)
E	< 180	< 15	< 47	Soft clay (sensitive sites)
F	—	—	—	Site-specific required: liquefiable, sensitive clay >3 m, peat >3 m, very high plastic

V_S30 is the time-averaged shear-wave velocity in the upper 30 m, computed as V_S30 = 30 / Σ(h_i / V_s,i). Site class enters the design response spectrum via F_a (short-period) and F_v (1-second-period) amplification factors.

9.2 Liquefaction screening (Youd-Idriss 2001, Boulanger-Idriss 2014)

A saturated loose-to-medium-dense sand can liquefy when cyclic shear stress raises pore pressure to σ’_v.

Cyclic Stress Ratio (CSR) — demand:

CSR = 0.65 · (a_max / g) · (σ_v / σ'_v) · r_d

with r_d (depth reduction) ≈ 1 - 0.00765·z (z < 9.15 m).

Cyclic Resistance Ratio (CRR) — capacity from (N₁)₆₀,cs:

CRR₇.₅ = 1/[34 − (N₁)₆₀,cs] + (N₁)₆₀,cs / 135 + 50/[10·(N₁)₆₀,cs + 45]² − 1/200

Factor of safety: FS_liq = (CRR / CSR) · MSF · K_σ · K_α, with magnitude scaling factor MSF (= 1 at M_w = 7.5), overburden K_σ, sloping-ground K_α.

FS_liq < 1.0 → liquefaction expected. CPT-based variant uses normalized q_c1N,cs (Boulanger-Idriss 2014, Liquefaction Susceptibility, Triggering, and Consequences).

9.3 Site-response analysis

• Equivalent-linear: SHAKE91 (Schnabel-Lysmer-Seed 1972), STRATA, DEEPSOIL (Hashash, UIUC). Iterates G, ξ to match strain.
• Nonlinear time-history: DEEPSOIL nonlinear, FLAC2D/3D with hysteretic damping (Itasca), PLAXIS Dynamics. Required for soft sites, large strain, or near-fault motions.

Output: surface acceleration time history → design spectrum that supersedes the code spectrum for site-specific projects (ASCE 7-22 §11.4.8 and §21).

10. Earth dams, levees, tailings

Zoned earth dam — central impervious core (CL or CH clay, sometimes asphaltic concrete or geomembrane), upstream and downstream transition (filter) zones, shells (rockfill, sand-gravel). Filter design (Bertram 1940, Sherard-Dunnigan 1985, USACE EM-1110-2-1901): D_15,filter / D_85,base < 4-5 (piping criterion), D_15,filter / D_15,base > 4-5 (permeability criterion).

Internal erosion modes: concentrated-leak erosion (Teton Dam 1976), backward piping erosion, suffusion (loss of fines through stable skeleton), contact erosion (flow along zone interface). ICOLD Bulletin 164 is the modern reference.

Tailings dams (waste from mining): three construction methods —

• Upstream: raise the crest by depositing tailings against the previous lift; cheapest, weakest. Brumadinho 2019 (Brazil, Fundão 2015, Mount Polley 2014 — upstream method now banned in Brazil and Chile).
• Centerline: raises follow the dam centerline; intermediate.
• Downstream: raises move downstream of original toe; strongest, most expensive.

Global Industry Standard on Tailings Management (2020) — UN-led post-Brumadinho framework with mandatory risk classification and independent review.

10b. Instrumentation and monitoring

Modern geotechnical projects instrument both during construction and in long-term service:

Instrument	Measures	Common use
Piezometer (vibrating-wire, standpipe, Casagrande)	Pore-water pressure	Dam, embankment, slope, excavation
Inclinometer	Lateral movement vs depth	Slope, excavation wall, dam
Settlement plate / magnetic extensometer	Vertical settlement	Embankment, surcharge fill
Strain gauge (rebar, sister bar, fibre-optic DFOS)	Stress in foundation element	Pile, anchor, tieback
Earth-pressure cell (Glötzl, Kulite)	Total earth pressure	Wall, tunnel lining
Tiltmeter	Rotation	Building monitoring during adjacent excavation
Crackmeter / jointmeter	Crack opening	Dam, retaining wall, historic structure
Total station / robotic survey / GNSS	Surface displacement	Slope, dam crest
InSAR (satellite radar)	Regional subsidence, mm/yr	Mexico City, Jakarta, San Joaquin Valley
Acoustic emission / micro-seismic	Crack initiation	Tailings dam, rock slope
DTS (distributed temperature sensing)	Seepage detection in embankment	Dam, levee

Observational method (Peck 1969 Rankine Lecture): design to a most-probable scenario, instrument to verify, and apply pre-defined contingency designs if measurements exceed thresholds. The cornerstone of modern dam and deep-excavation practice; used at the Heathrow Express tunnel collapse (1994) investigation and the Big Dig (Boston) cut-and-cover excavations.

10c. Rock mechanics adjacency

When the foundation bears on or excavation cuts through rock rather than soil, rock mechanics takes over with related but distinct frameworks:

• Rock-mass classification: RMR (Bieniawski 1973, 1989), Q-system (Barton-Lien-Lunde 1974, NGI), GSI (Hoek 1995). Combine UCS, RQD, joint spacing/condition, groundwater, and stress to a single score that maps to support requirements.
• Failure criteria: Hoek-Brown (Hoek-Brown 1980, 2002 update) for jointed rock mass; Barton-Bandis for joints; Mohr-Coulomb for intact rock or homogenized rock mass.
• Discontinuity-controlled stability: Markland test (planar, wedge, toppling), stereographic projection.
• Software: RS2/RS3 (Rocscience), 3DEC / UDEC (Itasca discrete-element), Phase² (legacy), Examine 2D/3D, FLAC for continuum rock, ROCFALL (rockfall trajectory), RocSlope, Dips (stereonet).
• In-situ stress: hydraulic fracturing (Hubbert-Willis 1957), overcoring (CSIRO HI cell), borehole breakouts. Required for tunnels, deep mines, repositories.
• Tunneling: NATM (New Austrian Tunneling Method, Rabcewicz 1964) for sequential excavation with shotcrete + rock-bolt support; TBM (tunnel boring machine) for long alignments; Q-system or RMR drives support class selection. See structural-analysis for tunnel lining design.

11. Tools / software

Category	Tools
Limit-equilibrium slope stability	SLIDE2 / SLIDE3 (Rocscience), GeoStudio SLOPE/W (Bentley/Seequent), Galena (Clover, free), Plaxis 2D LE module, Slope2 (Petros)
FE / FD geotechnical	PLAXIS 2D/3D (Bentley), FLAC2D / FLAC3D (Itasca), Abaqus geotech, Midas GTS-NX, RS2 / RS3 (Rocscience), OpenGeoSys
Seepage / consolidation	GeoStudio SEEP/W + SIGMA/W, Plaxis Flow, Settle3 (Rocscience), Bentley SVOFFICE 5/AIR
Liquefaction	NCEERLiq (free spreadsheets), LiquefyPro, CLiq (GeoLogismiki, CPT-based)
Site response	SHAKE91 / SHAKE2000, DEEPSOIL (Hashash UIUC, free), STRATA (UT Austin, free)
Pile design	DFSAP, LPILE (Ensoft, lateral), GROUP (Ensoft, pile groups), APile (Ensoft, axial), GeoStudio PILE3D
Retaining wall	RetainPro, WallCAP, Plaxis 2D for staged excavation
MSE wall	MSEW (ADAMA), ReSSA (geosynthetic-reinforced slope), MSE+
Boring-log / data management	gINT (Bentley), HoleBase SI (Keynetix), GeoSuite (Trimble), Bentley OpenGround
BIM integration	Bentley OpenGround Cloud, Civil 3D + Subsurface Utility Engineering, Tekla Civil
In-situ data interpretation	CPeT-IT (GeoLogismiki), Novo-CPT, GeoLogger
Rock mechanics	RS2/RS3, 3DEC, UDEC, Dips, Swedge, RocPlane, RocFall (Rocscience/Itasca)
Open-source	OpenGeoSys, FEniCS-based GeoChron, Code_Aster geotech modules, Salome-Meca

11.1 Solver paradigms

Paradigm	Strengths	Weaknesses	Representative
Limit equilibrium (LEM)	Fast, well-validated, code-familiar	Assumes slip surface; no displacement output	SLIDE, SLOPE/W
Finite element (FE)	Arbitrary geometry, constitutive flexibility, deformation output, strength-reduction FS	Mesh dependence, runtime, parameter calibration	PLAXIS, RS2
Finite difference (FD)	Explicit dynamic, large strain, contact	Smaller commercial ecosystem	FLAC2D/3D
Discrete element (DEM)	Joint-controlled rock, granular flow	Calibration of micro-parameters	PFC, 3DEC, YADE
Material-point / SPH	Very large deformation (landslides, debris flow)	Specialized research codes	Anura3D, GeoFlow-SPH

11.2 Reporting and data exchange

• gINT (Bentley): legacy boring-log + lab-data database, exports to Word/PDF.
• HoleBASE SI (Keynetix/Bentley): cloud-friendly successor with GIS integration.
• OpenGround Cloud (Bentley): SaaS replacement; AGS / DIGGS / IFC export.
• AGS format (Association of Geotechnical Specialists, UK): de-facto European standard for geotechnical data interchange (current AGS4.1, 2022).
• DIGGS (Data Interchange for Geotechnical and GeoEnvironmental Specialists, USA): ASCE-backed XML schema; growing AASHTO adoption.

11b. Engineering judgement and FS calibration

Soil parameters carry CoV of 0.2-0.6 (compared with ~0.05 for steel σ_y). The global factors-of-safety quoted across this note are not arbitrary — they are calibrated to that parameter uncertainty and to load uncertainty:

Design situation	FS (global)	LRFD equivalent (φ / γ)	Rationale
Bearing capacity, shallow	3.0	φ = 0.45-0.50 (AASHTO)	Combined φ’ or s_u uncertainty + bearing-factor approximation
Pile axial, static analysis	2.5-3.0	φ = 0.35-0.40	High parameter uncertainty in skin-friction correlations
Pile axial, static load test	2.0	φ = 0.55-0.65	Direct verification reduces uncertainty
Slope, drained long-term	1.5	(n/a)	Catastrophic consequence, parameter uncertainty
Slope, end-of-construction	1.3	(n/a)	Short exposure period, controlled fill
Slope, seismic pseudo-static	1.0-1.1	(n/a)	Rare event, Newmark displacement allows yielding
Retaining wall, sliding	1.5	(n/a)	Limited consequence (deformation, not collapse)
Retaining wall, overturning	2.0	(n/a)	Toppling = collapse
Retaining wall, bearing	3.0	(n/a)	As shallow foundation
Dam, steady seepage	1.5	(n/a)	High consequence, well-characterized condition
Dam, rapid drawdown	1.1-1.3	(n/a)	Transient, less well predicted
Hydraulic heave / piping	1.5-2.0	(n/a)	Sudden failure mode, limited warning

Characteristic-value selection (EN 1997-1 §2.4.5.2): take a “cautious estimate of the value affecting the occurrence of the limit state”. In practice, ~the 5th-percentile lower bound for strength parameters, the 95th-percentile upper bound for unfavorable loads. Modern probabilistic geotechnical design (FORM, Monte Carlo, random-field models — Vanmarcke 1977, Fenton-Griffiths 2008) replaces single FS values with reliability index β ≥ 3.0 (P_failure ≤ 10⁻³) for ordinary structures, β ≥ 4.0 for major dams.

Peck 1969 Rankine Lecture three rules: (1) “Bring all available facts to bear on the problem”; (2) “Use the simplest method that fits the case”; (3) “Wherever practicable, use the observational method”. Sixty years on, they still organize good practice better than any code clause.

12. Cross-references

• mechanics-of-materials — stress and strain framework; effective-stress decomposition.
• structural-analysis — foundation reactions feed structural model; soil-springs (Winkler) coupling.
• structural-dynamics (planned) — earthquake-engineering counterpart; modal analysis with soil-structure interaction.
• fluid-mechanics (planned) — Darcy seepage, well hydraulics underpinning groundwater flow.
• materials-steel — sheet piles, H-piles, micropile casing.
• reinforced-concrete (planned) — footings, drilled shafts, retaining walls.
• fem-fea (planned) — geotechnical FE conventions (PLAXIS, FLAC) and constitutive models (Mohr-Coulomb, Hardening Soil, Cam-Clay).
• cfd-deep (planned) — seepage and dam-break flows.
• transportation-engineering (planned, same batch) — pavement subgrade, CBR, resilient modulus M_R.
• agricultural-robotics — terrain trafficability (Bekker-Wong), wheel slip on weak subgrade.
• scientific (planned) — AGS (Association of Geotechnical Specialists), DIGGS (Data Interchange for Geotechnical and GeoEnvironmental Specialists), gINT .gpj.

13. Citations

1. Craig, R. F.; Knappett, J. A. Craig’s Soil Mechanics, 9th ed., CRC Press, 2019. ISBN 978-1138070066. Canonical UK undergraduate text; equally strong in classical and critical-state frameworks.
2. Das, B. M.; Sivakugan, N. Principles of Geotechnical Engineering, 10th ed., Cengage, 2022. ISBN 978-0357420485. Most-adopted US undergraduate text.
3. Bowles, J. E. Foundation Analysis and Design, 5th ed., McGraw-Hill, 1996. ISBN 978-0079122476. The reference for shallow and deep foundations.
4. Lambe, T. W.; Whitman, R. V. Soil Mechanics, Wiley, 1969 (SI version 1979). ISBN 978-0471511922. Canonical, dated but still cited.
5. Terzaghi, K. “Die Berechnung der Durchlässigkeitsziffer des Tones aus dem Verlauf der hydrodynamischen Spannungserscheinungen.” Sitzungsberichte Akademie der Wissenschaften, Wien, 1923. Original 1-D consolidation theory.
6. Terzaghi, K. “Erdbaumechanik auf bodenphysikalischer Grundlage.” Deuticke, Vienna, 1925. Original effective-stress principle.
7. Terzaghi, K. Theoretical Soil Mechanics. Wiley, 1943. The codification of the discipline.
8. Terzaghi, K.; Peck, R. B.; Mesri, G. Soil Mechanics in Engineering Practice, 3rd ed., Wiley, 1996. ISBN 978-0471086581.
9. Coulomb, C. A. “Essai sur une application des règles de Maximis & Minimis à quelques Problèmes de Statique.” Mémoires de Mathématique et de Physique, Acad. Sciences, Paris, 1776. Original Mohr-Coulomb shear law and active-earth-pressure wedge.
10. Mohr, O. “Welche Umstände bedingen die Elastizitätsgrenze und den Bruch eines Materials?” Zeitschrift des Vereins Deutscher Ingenieure, vol. 44, 1900. Mohr’s failure envelope.
11. Meyerhof, G. G. “Some Recent Research on the Bearing Capacity of Foundations.” Can. Geotech. J., vol. 1, no. 1, 1963, pp. 16-26. Bearing-capacity factor N_γ and shape/depth/inclination correction factors.
12. Skempton, A. W. “The Pore-Pressure Coefficients A and B.” Géotechnique, vol. 4, no. 4, 1954, pp. 143-147. Effective-stress pore-pressure parameters.
13. Skempton, A. W. “The φ = 0 Analysis of Stability and Its Theoretical Basis.” Proc. 2nd ICSMFE, Rotterdam, 1948.
14. Casagrande, A. “Classification and Identification of Soils.” Trans. ASCE, vol. 113, 1948, pp. 901-930. USCS and A-line plasticity chart.
15. Bishop, A. W. “The Use of the Slip Circle in the Stability Analysis of Slopes.” Géotechnique, vol. 5, no. 1, 1955, pp. 7-17. Bishop’s simplified method.
16. Janbu, N. “Earth Pressure and Bearing Capacity Calculations by Generalized Procedure of Slices.” Proc. 4th ICSMFE, London, 1957.
17. Spencer, E. “A Method of Analysis of the Stability of Embankments Assuming Parallel Inter-Slice Forces.” Géotechnique, vol. 17, no. 1, 1967, pp. 11-26.
18. Morgenstern, N. R.; Price, V. E. “The Analysis of the Stability of General Slip Surfaces.” Géotechnique, vol. 15, no. 1, 1965, pp. 79-93.
19. Robertson, P. K. “Soil Classification Using the Cone Penetration Test.” Can. Geotech. J., vol. 27, no. 1, 1990, pp. 151-158. The CPT soil-behaviour-type chart.
20. Youd, T. L.; Idriss, I. M. “Liquefaction Resistance of Soils: Summary Report from the 1996 NCEER and 1998 NCEER/NSF Workshops on Evaluation of Liquefaction Resistance of Soils.” J. Geotech. Geoenv. Eng., ASCE, vol. 127, no. 10, 2001, pp. 297-313.
21. Boulanger, R. W.; Idriss, I. M. CPT and SPT Based Liquefaction Triggering Procedures. Report UCD/CGM-14/01, University of California, Davis, 2014.
22. Sherard, J. L.; Dunnigan, L. P. “Filters and Leakage Control in Embankment Dams.” Proc. Symp. on Seepage and Leakage from Dams and Impoundments, ASCE, 1985.
23. Roscoe, K. H.; Schofield, A. N.; Wroth, C. P. “On the Yielding of Soils.” Géotechnique, vol. 8, no. 1, 1958. Foundations of critical-state soil mechanics.
24. Schofield, A. N.; Wroth, C. P. Critical State Soil Mechanics. McGraw-Hill, 1968.
25. Newmark, N. M. “Effects of Earthquakes on Dams and Embankments.” Géotechnique, vol. 15, no. 2, 1965, pp. 139-160. Newmark sliding-block.
26. ASTM D2487-17 — Standard Practice for Classification of Soils for Engineering Purposes (Unified Soil Classification System).
27. ASTM D1586-18 — Standard Test Method for Standard Penetration Test (SPT) and Split-Barrel Sampling of Soils.
28. ASTM D3441-16 / D5778-20 — Cone Penetration Testing of Soils.
29. ASTM D2435-11 — Standard Test Methods for One-Dimensional Consolidation Properties of Soils Using Incremental Loading.
30. ASTM D4767-11 — Consolidated Undrained Triaxial Compression Test for Cohesive Soils.
31. ASTM D2850-15 / D2166-16 — Unconsolidated-Undrained Triaxial and Unconfined Compression.
32. ASTM D4318-17 — Liquid Limit, Plastic Limit, and Plasticity Index of Soils.
33. ASTM D1557-12 — Modified Proctor Compaction.
34. ASTM D1143-20 / D4945-17 / D7383-19 / D8169-22 — Static, High-Strain Dynamic, Statnamic, and Bidirectional Pile Load Tests.
35. ASCE 7-22 — Minimum Design Loads and Associated Criteria for Buildings and Other Structures, Chapters 11-21 (seismic).
36. ASCE 41-23 — Seismic Evaluation and Retrofit of Existing Buildings.
37. IBC 2024 — International Building Code, Chapter 18 (Soils and Foundations).
38. EN 1997-1:2024 — Eurocode 7: Geotechnical Design — Part 1: General Rules.
39. AASHTO LRFD Bridge Design Specifications, 10th ed., 2024, Section 10 (Foundations) and Section 11 (Abutments/Walls).
40. USACE EM-1110-2-1901 — Seepage Analysis and Control for Dams. US Army Corps of Engineers.
41. API RP 2GEO — Geotechnical and Foundation Design Considerations (offshore). American Petroleum Institute.
42. ICOLD Bulletin 164 — Internal Erosion of Existing Dams, Levees and Dikes, and Their Foundations. International Commission on Large Dams.
43. Global Industry Standard on Tailings Management, ICMM / PRI / UNEP, 2020. Post-Brumadinho framework.
44. PLAXIS 2D/3D Reference Manuals (Bentley Systems). FLAC2D/3D User’s Manual (Itasca). GeoStudio SLOPE/W, SIGMA/W, SEEP/W User Documentation (Bentley/Seequent). SLIDE2/SLIDE3 + RS2/RS3 Manuals (Rocscience).