Every analysis. Every test.No black boxes.

Strip 2 m, Df 1.5 m, c′ 10 kPa, φ′ 30°, γ 18 kN/m³

q_ult ≈ 1,210 kPa → q_safe ≈ 400 kPa (FoS 3), every N-factor cited

q 150 kPa, B 2 m, Es 25 MPa, 4 m NC clay

Immediate 8 mm + consolidation 22 mm = 30 mm

Footings 30 / 12 / 22 / 8 mm on a 6 × 6 m grid

Governing β = 1/333, tilt 1/520, within framed 1/300 ✓

q 120 kPa over a qc profile, B 2.5 m, 30-yr

s ≈ 19 mm with depth + creep correction

Cv 3 m²/yr, H_dr 2 m, U 90 %

t ≈ 1.1 yr (Tv 0.848)

Tv 0.2; target U 90 %

U 50.5 % at Tv 0.2; Tv 0.848 needed for U 90 %

Phosphate-clay slurry H₀ 9.6 m, e₀ 14.8, power-law e-σ′ / k-e (Townsend-McVay 1990)

Ultimate settlement 5.32 m by the nonlinear PDE — within 2.2% of the published CONDES/FSConsol symposium result (5.44 m); log-linear or power-law constitutive

Soft slurry (C_c 2.4, e₀ 5) over stiffer clay (C_c 0.8, e₀ 3), H₀ 6 m

Interface flux in the continuous σ′ gradient (harmonic-mean k) — e jumps at the boundary, σ′ continuous; reduces exactly to the single-material engine within a layer

E 5 MPa, ν 0.3, k 1e-4 m/day, 5 m layer double-drained, σ 100 kPa

Settlement 74 mm (σ·H/E_oed), c_v ≈ 0.069 m²/day derived from k & E_oed, t₉₀ ≈ 77 days — coupled poroelastic solve, U–Tv matches Terzaghi

6×6 m loaded area, q 100 kPa, 10 m clay, E′ 5 MPa, ν′ 0.3, k 1e-8 m/s, top drainage

Final 93.3 mm (62.0 immediate + 31.3 consolidation); computed Skempton-Bjerrum μ 0.41; t₅₀ 3.1 days against 33.2 by 1-D Terzaghi — 10.7× faster because water escapes sideways. Collapses to q·H/E_oed exactly when the far field is set to 0

2 columns 800 + 1200 kN at 4 m, qa 150 kPa

L 6.4 m, resultant centred (e 0), B 2.1 m

Σ load 24 MN, qa 150 kPa

Raft 13 × 13 m, q 142 kPa < qa ✓

k 30 MN/m³, 0.5 m slab, 8 columns

Max settlement 18 mm, M_max 420 kN·m/m

EI, k 20 MN/m³, point load 200 kN

λ 0.62 /m, y_max 4.1 mm, M_max 81 kN·m

B 2 m, Es 20 MPa, ν 0.3

k_s ≈ 11.8 MN/m³ (Vesić) for the STAAD / ETABS hand-off

0.3 m plate, 12 mm settlement at 220 kPa

Safe BP 147 kPa, scaled to the footing width

A 6 m², 20 t block, Cu 4×10⁴ kN/m³, 25 Hz

f_n 17.4 Hz, ratio 1.43 — clear of resonance ✓

SPT profile, Df 2 m, silty sand, B = 1 → 3 m

Allowable pressure per size = min(shear, settlement), governing mode flagged

N 21, φ′ COV 0.12, B 2 m, Df 8 m, demand 250 kPa

Characteristic SBC (P05), reliability 96 %, β 1.8

Dense sand φ 40° (1.5 m) over soft clay c_u 30, B 1.5 m

q_ult 459 kPa by punching shear (q₂/q₁ 0.11, Ks 2.5)

B 2 m, Df 1 m, φ′ 30°, slope 20° at the crest

q_ult 529 kPa — 51 % of level-ground capacity retained

q′ 100 kPa, B 3 m, average SPT N̄ 12, normal sand

Immediate 11.4 mm, with creep 14.8 mm (z_I 2.28 m)

q 150 kPa, 3 m square, Es 20 MPa, ν 0.3, H 6 m

Centre 17.6 mm (Steinbrenner I_s 0.43, F1/F2 closed-form)

q 100 kPa, 1 × 1 m, z 1 m, centre, ν 0

Δσ_z 33.6 kPa (Boussinesq) vs 21.6 kPa (Westergaard, layered)

q 100 kPa, R 2 m, z 3 m (centre)

I 0.424 → Δσ_z 42.4 kPa

q 100 kPa, B 2 m, z 1 m (centreline)

I 0.818 → Δσ_z 81.8 kPa (vs 66.7 by 2:1)

Q 100 kN/m, x 0, z 2 m

Δσ_z 31.8 kPa (I 0.637); σ_x = τ = 0 on the centreline

Cα 0.04, e_p 1.0, H 4 m, t₁ 2 yr → t₂ 50 yr

Cαε 0.02 → creep S_s 112 mm over 1.4 log-cycles

S_oed 100 mm, A 0.7, α 0.7, S_imm 15 mm

μ 0.91 → field S_c 91 mm, total 106 mm

Q 1000 kN, M 100 kN·m, 2 × 2 m

e 0.1 m < B/6 → q 325 / 175 kPa, no uplift, B′ 1.8 m

22.4 × 4.5 m raft, p 140, soil 0.5 m Es 49.5 + rock 8.5 m Es 248.7

σz = 4·p·I_B per layer → 3.9 mm total (rigidity × depth corrected)

Basement 20 × 30 m, base 5 m, water table 1 m

Uplift 23,544 kN, FoS 2.55, EN 1997-1 UPL util 0.44

q_gross 200 kPa, Df 5 m, γ 18 kN/m³

relief 90 kPa → net 110 kPa, 45 % compensated (settlement governs)

Deflections 1.2/1.4/1.0/1.6/1.3 mm, major road

x̄ 1.30, σ 0.224 → Dc 1.747 mm (read overlay off the IRC 81 curve)

Strip 2 m, sᵤ 20 kPa, φ 0 (undrained)

q_ult = 102.9 kPa (Prandtl 5.14·sᵤ to 0.1%) + the full load–settlement curve & collapse mechanism

Strip 2 m, cᵤ 50 kPa, φ 0 (undrained)

Rigorous two-sided bound 4.07·cᵤ ≤ q_exact ≤ 6.00·cᵤ, bracketing the exact Prandtl 5.14·cᵤ — singularity-immune

Strip B 2 m, c′ 10, φ 25°, E_ref 30 MPa, m 0.5

Full load–settlement curve + q_ult from a meshed plane-strain continuum (general-stress Mohr-Coulomb strength + HS stress-dependent stiffness, B-bar anti-locking), cross-checked live against the closed-form Vesić N-factors — a PLAXIS/RS2-class footing BVP

Square B 2 m, sᵤ 50 kPa, φ 0 (undrained)

q_ult + full load–settlement curve from a true 3-D continuum (quarter-symmetry, 20-node serendipity hexahedra, viscoplastic Mohr-Coulomb) capturing the square/circular shape effect (s_c≈1.2) a 2-D model cannot — cross-checked live against Skempton/Vesić; heavy solve on Modal — a PLAXIS-3D/RS3-class footing BVP

Strip B 2 m, D_f 1 m, c′ 10, φ′ 30°, E₅₀ʳᵉᶠ 30 MPa, m 0.5

The FULL load–settlement curve from the true HS constitutive law integrated at every Gauss point (hyperbolic pre-failure response, stress-dependent E(σ₃), per-point plastic shear hardening γ^p) + q_ult cross-checked live against the Vesić closed form — 28 cited literature anchors: Prandtl 5.14·sᵤ reproduced from above with q_ult/sᵤ constant to 0.7 % over an 8× strength range, Vesić c·N_c + q₀·N_q matched to ~2–5 % over a 20× surcharge range, and monotone mesh convergence to the exact limit

E₅₀ʳᵉᶠ 30 MPa, m 0.5, c′ 1, φ 35°, σ₃ 100 kPa

Stress-dependent E₅₀/E_ur, hyperbolic q–ε₁ to q_f 273 kPa (secant = E₅₀ exactly at half-strength) + oedometer E_oed — calibrate HS parameters against your lab curves

5 m NC clay, Δq 100 kPa, σ′v0 50 kPa, E_oedʳᵉᶠ 4 MPa, m 0.9, φ 25°

Nonlinear settlement 135 mm with stress-dependent stiffness (secant E_oed 3.8 MPa) — vs 233 mm from a fixed initial modulus; OCR 2 halves it (stiff E_ur reload)

3-layer profile (soft 3 m / firm 4 m / stiff 5 m), Δq 120 kPa, WT 2 m

Total 253 mm; each sub-layer an oedometer at its own σ′v0 + HS params + OCR, auto sub-discretised (discretisation-independent) — soft shallow layer contributes 189 mm (the dominant stratum for ground improvement)

600 mm bored, 15 m, c_u 50 kPa

Q_ult ≈ 1,850 kN → Q_safe 740 kN (FoS 2.5); tension T_safe from shaft + self-weight

1 m bored pile, M30, 8000 mm² steel

M_n, M_cr, M_y + the COMPUTED cracked-EI (not a 0.35–0.7 guess) for the p-y solver

1 m bored pile, M30, 8000 mm² steel

Full P–M failure envelope: squash 19,860 kN, balance, pure-bending M_n — check any (M, P) demand

3×3 group, s 2 m, V 300 kN, M 1200 kN·m

Per-pile axial 133 kN (leeward) to −67 kN (uplift), cap stiffness — statics-validated

3 helices 0.3 m at 5/4/3 m, φ 32°, γ′ 10

Σ plate bearing 197 kN + shaft → Q_ult 214 kN; torque-checked

1 m × 15 m, c_u 100 kPa (α-method)

Side 2180 kN + base 707 kN → Q_ult 2884 kN

0.2 m bond, 8 m, α 150 kPa, 3000 mm² steel

Bond allow 302 kN vs structural 957 kN → 302 kN governs

20 m steel pile, 50 kN ram, 100 kJ, Rᵤ 1500 kN

Set 24 mm → 41 blows/m, σ_c 253 MPa (bearing graph)

P 1500 kN, 0.4 m column, d 0.5 m, M25, q 240 kPa

τv 0.73 MPa ≤ τc 1.25 MPa → util 0.58 ✓

3×3 group, d 0.5 m, L 15 m, s 1.5 m, w_single 8 mm

r_m 26 m → Rs 5.6 → group settlement 45 mm

9 piles, 3 d c/c spacing

η 0.74 (Converse-Labarre) → group 12.3 MN

600 mm, soft clay ε50 0.02, 150 kN head

Groundline 5.5 mm, M_max −258 kN·m (FDM)

0.5 m pile, e 1 m, My 200 kN·m, clay cu 50 kPa

Hu 101 kN, hinge at 1.2 m (long-pile yield-governed)

30 kN ram, 1.2 m drop, 5 mm/blow set

R_u 1,731 kN → safe 692 kN

Fill over soft clay, neutral plane 9 m

Drag load 380 kN added at the neutral plane

Raft + 16 piles, 30 MN

α_pr 0.7, settlement 24 mm, 62 % carried by piles

500 mm × 15 m, maintained-load curve

Safe 1,333 kN (IS ⅔ @ 12 mm), Davisson ult 2,209 kN

6 m well, 6 m grip, H 1,500 kN, M 9,000 kN·m

K_p 6.11, elastic demand 98 > capacity 64 → revise

Group 3 × 3 m, 12 m friction piles, Q 4 MN, m_v 0.2

Settlement 133 mm (raft at 8 m, 2:1 spread Δσ′ 111 kPa)

Q 500 kN (40 % point), 15 m × 0.5 m, q_p 4 MPa

Head settlement 5.7 mm = 1.4 (elastic) + 4.0 (point) + 0.4 (shaft)

0.6 m × 15 m bored pile, clay s_u 60 kPa, 900 kN working

Q_ult 2,150 kN (shaft 72 %), 7.4 mm at working load

3×2 group of 0.6 m piles at 3D in sand, 1,200 kN cap load

9.8 mm cap deflection, Gₑ 0.66; leading row governs at 468 kN·m

0.6 m × 15 m free-head pile in sand, 200 kN operating shear

K22 3.1×10⁴ kN/m, K33 1.4×10⁵ kN·m/rad, coupling K23; symmetric to <1%

Ø600 pipe, 20 mm wall, fy 355 MPa

My 1,816 kN·m, Mp 2,389 kN·m (= fy·Z), shape factor 1.32

12 m slope, 1.5:1, c′ 15 kPa, φ′ 28°, r_u 0.3

FoS 1.38 (Spencer), critical circle located

β 20°, z 2 m, c′ 5 kPa, φ′ 30°, full seepage

FoS 1.12 (parallel seepage)

30 m face 60°, joint dips 35°, c 50 kPa, φ 30°

FoS 1.28 dry → 0.88 with water + seismic

30 m face 60°, 1000 kg block, μ 0.40, Rₙ 0.35, Rₜ 0.85

runout 16.9 m, max bounce 2.1 m, 227 kJ at the toe; Ritchie ditch 8.7 m × 1.8 m

15 m dam, 1:2.5 upstream, c' 5 kPa, φ' 28°, R-env φR 20°, pool 13 m → 0

FoS drops from the full-reservoir value to the after-drawdown value (3rd/undrained stage governs); Duncan-Wright-Wong τff interpolation

JRC 10, JCS 50 MPa, φr 30°, σn′ 500 kPa

φpeak 50° (i = 20° dilation), τ = 596 kPa — nonlinear envelope

K 300, n 0.5, c′ 10, φ′ 30°, Rf 0.9, σ₃ 100 kPa

(σ₁−σ₃)f 234.6 kPa, Ei 30.2 MPa, hyperbolic q(ε) → qult 260.7 kPa

φcs 25.4° (M 1.0), λ 0.16, κ 0.03, p′₀ 200 kPa

su 57.0 kPa (su/p′₀ 0.285), critical state p′ 114, q 114 kPa

G₀ 100 MPa, γ₀.₇ 2e-4, Gur 25 MPa

Gs = 72.2 MPa (0.722·G₀) at γ₀.₇; decays G₀→Gur with strain

c' 10, φ' 30°, σ₃ 100 kPa

triaxial failure 234.6 kPa (= Mohr-Coulomb), α 0.231, k 12.0 kPa

σ 200/100/100 kPa, σy 150 kPa

q = 100 kPa (√3J₂) < σy → elastic, FoS 1.50

suA 60, suP/suA 0.4, suDSS/suA 0.6

suA 60, suP 24, suDSS 36 kPa; isotropic q = 2suA = 120 kPa

Cc 0.3, Cs 0.05, Cα 0.01, e₀ 1.0, φcv 25°

λ* 0.065, κ* 0.022, μ* 0.00217, M 0.984, creep 0.5%/decade

ky 0.1 g, Ts 0.3 s, Sa 0.5 g, Mw 7.5

D₅₀ 18.5 cm (16–84%: 9.6–35.8 cm)

β 25°, c′ 10±30%, φ′ 28±10%, γ 19

μ_FoS 1.60, reliability index β, Pf (FOSM ≈ Monte-Carlo)

30 m soil column over Vs 600 rock

Transfer function → T₀ + peak amplification (eq-linear)

Zone IV, medium soil, T 0.5 s, R 5

Sa/g 2.50 → Ah 0.06 (ZPA 0.12 g)

ASCE 7-16, site B, Sₛ 1.5, S₁ 0.6, Vs30 800

SDS 0.90 g (Sa @ 0.2 s), SD1 0.32 g (Sa @ 1.0 s) — pick any code (IS / ASCE / EC8), no region gate

s_u,vane 50 kPa, PI 40 %

μ 0.835 → design s_u 41.7 kPa

6 m fill on soft clay c_u 20 kPa

FoS 1.31 (Ladd) — sets the stage-construction band

Side-hill fill, 1 m benches

Interface FoS 1.45

PGA 0.24 g, yield k_y 0.12 g

Permanent slip 4.6 cm

10 m slope 2:1, c′ 15 kPa, φ′ 25°, γ 19

FoS by φ-c reduction on a finite-element mesh (no assumed slip surface)

10 m slope 2:1, c′ 10 kPa, φ′ 20°, γ 20, finite width B/H = 1

F₃D by 3-D φ-c reduction — the failure mechanism emerges (no assumed slip surface); end restraint gives F₃D ≈ 1.15·F₂D, converging to the 2-D value as the slide widens

A real terrain grid (DEM), multi-material soil, thousands of spherical trial surfaces

the 3-D-critical failure mass anywhere on the terrain — F₃D, the sphere, its volume/area/footprint — reproducing the parametric slope-3d circle on a planar slope (validated to within the 3-D end-restraint credit)

5 m wall, φ′ 32°, kh 0.1

Ka 0.31, Pa 56 kN/m; Kae 0.41 (Mononobe-Okabe)

φ′ 30°, OCR 4, γ 18, H 5 m

K0 1.00 (vs 0.50 NC), at-rest thrust 225 kN/m

5 m cantilever, 10 kPa surcharge

FoS overturn 2.4, slide 1.7, resultant in kern ✓

Cantilever 6 m retained, φ′ 30°

Embedment 4.2 m, M_max 185 kN·m/m

8 m cut in soft clay

Strut loads from apparent pressure; base-heave FoS 1.4

10 m cut, 15×30 m, s_u 40 kPa, γ 18, q 10

N_c 6.41 → FoS 1.35 (Bjerrum-Eide) — deepen toe / improve clay

He 10 m, δh,max 30 mm (sand), building at 5 m

δv,max 30 mm, trough to 20 m, 22.5 mm at building (1/667)

0.15 m hole, 8 m bond, c_u 100 kPa, α 0.4

τ 40 kPa → T_ult 151 kN, allowable 75 kN (FoS 2)

6 m propped wall, prop at 1.5 m

Deflection 13 mm, M_max 156 kN·m/m, prop 80 kN/m, passive 38% mobilised

6 m dig, Ø600 diaphragm wall, 6 m embedment, prop at 1.5 m

Deflection 4 mm, M_max 132 kN·m/m, prop 88 kN/m, passive 40% mobilised; LEM cross-check agrees (≥ 3.58 m)

9 m retained, 600 mm piles

Embedment 5.1 m, M 420 kN·m, deflection 22 mm

10 m, 750 mm secant

Embedment 5.6 m, water cut-off achieved ✓

8 m, geogrid at 0.6 m spacing

T_max 24 kN/m, pullout FoS 1.6, sliding 1.8

9 m cut, nails on a 1.5 m grid

Global FoS 1.5, nail tension 95 kN

φ 35°, R_inter 0.67 (concrete/sand), σ′_n 100 kPa

δ 25.1°, τ_max 46.9 kPa — only 67% of the soil strength; the reduced wall/shaft friction to design with

Wide cut, cᵤ 30 kPa, γ 18, excavate to 8 m in 6 lifts

Base heave builds 18→62 mm per lift then basal-heave collapse near 6.7 m (N≈4.8, conservative vs Prandtl 5.14) — the staged deformation a closed-form check can’t give

Δh 6 m, 4-well system

Q 1,150 m³/day (Thiem), drawdown to formation

Zoned dam, k profile

Phreatic line + exit gradient 0.42 < critical

L 30 m, h₁ 12 m, h₂ 3 m, k 10⁻⁵

Phreatic line + q within ~5 % of the exact Dupuit q, seepage face located

Homogeneous 20 m dam

Casagrande line, q 1.8×10⁻⁵ m³/s per m

Falling-head in cased borehole

k 3.2×10⁻⁶ m/s (Hvorslev)

30 min for a 25 mm drop

Perc rate → soak-field sizing

PVD 1 m grid, Cv 2 m²/yr

90 % consolidation in ~4 months (Hansbo)

70 kPa vacuum, 8 m clay, PVD 1.5 m, 0.5 yr

63 kPa eff. (replaces 3.5 m fill) → 657 mm primary, U 74 %

2-layer NC profile, Δσ 40/30, cv 1.5/2.0

Total 190 mm; U 95.6 % at 2 yr (settlement-weighted)

Plate readings 100…433 mm at equal Δt

Final 500 mm, U 86.6 %, 67 mm remaining

Head 2 m, ΣL_v 14 m, ΣL_h 30 m, fine sand

Lane C_w 12 ≥ 7 ✓, Bligh C_B 22 ≥ 15 ✓ — safe against piping

D10 0.2 mm, void ratio 0.7, 20 °C

k 4×10⁻⁴ m/s (Hazen), 4.3×10⁻⁴ m/s (Kozeny-Carman)

Gs 2.65, e 0.65, Δh 3 m over L 6 m

i_cr 1.00, i_e 0.50 → FoS 2.0 against boiling (γ′ 9.81)

Vs30 / SPT profile to 30 m

Site class D → design response spectrum

H 30 m, Vs 200 m/s, ξ 5 %, rock Vs 760

T₀ 0.60 s, peak amplification ×3.6, surface PGA from rock

H 30 m, Vs 200 m/s, τ_max 80 kPa, rock PGA 0.02 → 0.4 g

Weak motion amplifies ×1.8; strong motion DE-amplifies to ×0.8 (soil softens + hysteretic damping) — the nonlinearity equivalent-linear misses

Sediment basin, H 30 m, soil Vs 200 / rock Vs 760 m/s, ξ 5%

2-D basin focusing amplifies the surface ×1.8 MORE than a 1-D column (Mexico City / Kobe effect) — validated to 2-D/1-D = 1.00 on a flat profile

Ridge H 20 m, half-width 50 m (slope ~22°), Vs 500 m/s

Crest topographic factor S_T ≈ 1.4 — the hilltop shakes 40% harder than flat ground, purely from geometry (validated flat S_T = 1.00, bounded < Trifunac 2)

H 15 m, Vs 140 m/s, WT 1 m, FC 5 %, bedrock PGA 0.30 g, 2 Hz, 12 s, v = 1

Liquefaction at t = 3.37 s, peak r_u 0.992. AFTER triggering the surface peak collapses to 0.024 g against the 0.156 g a total-stress solve on identical inputs gives (−84.8 %), the late-window RMS to 3.5 %, and the site period lengthens 1.23× — the recorded Port Island / Wildlife Array de-amplification signature that a total-stress site response plus a separate triggering check structurally CANNOT produce. Before triggering the two runs agree, so the coupling is shown to act only where the physics says it should; both are reported side by side

N 15, FC 5 %, σ′v 66 kPa, PGA 0.24 g, M 7.5

CRR 0.186, CSR 0.257 → FoS 0.72 → liquefiable

qc 5 MPa, FC 10 %, σ′v 60 kPa, z 5 m, amax 0.3 g, Mw 7.0

qc1Ncs 73, CRR 0.134, CSR 0.307 → FoS 0.47 (liquefies)

Vs 180 m/s, FC 10 %, σ′v 80 kPa, z 5 m, amax 0.3 g, Mw 7.0

Vs1 190, CRR 0.193, CSR 0.234 → FoS 0.98 (marginal)

D 6 m, axis 15 m, volume loss 1 %, K 0.5 (clay)

i 7.5 m, Smax 15.0 mm, 6.2 mm at 10 m offset, slope 1.2 mm/m

Ns 0.18, c 20 kPa, γ 18 kN/m³, H 6 m

c_d 19.4 kPa → FoS 1.03, critical height 6.2 m

H 30 m, Vs 250 m/s, ky 0.1 g, kmax 0.2 g, norm 0.05 s

T0 0.31 s, ky/kmax 0.5 → crest displacement 31 mm

4 % cement, γd 2000 kg/m³, 7-day UCS 5.0 MPa, CTB

binder 80 kg/m³, target 4.5–7.0 MPa → accepted

CVPD 100, CBR 5 %, total 350 mm (curve C)

curve C → base 225 mm + sub-base 125 mm, bituminous surfacing

Aircraft ACN 45, pavement PCN 50, flexible

ratio 0.90 ≤ 1 → unrestricted operations

Flexible: ESWL 30000 lb, p 100 psi, CBR 8, 5000 coverages

Corps CBR → 19.2 in cover (α 1.001); rigid slab via Westergaard edge

εt 70 µε, E 500 ksi, Hac 6 in, Va 7 %, Vbe 11 %, N 1e7

C 0.415, Nf 1.01e9 → damage 0.99 % → 0.59 % area cracking

3-layer AC/base/subgrade, E 500/25/7.5 ksi, h 4/8 in, q 100 psi, a 5 in

εt 346 µε (fatigue) · εv 942 µε (rutting) · deflection 0.71 mm — exact-Boussinesq-validated

3-layer section, εt 346 µε, εc 942 µε, E 500 ksi, 1e5 ESALs

Nf 2.65e5 (fatigue) · Nr 4.82e4 (rutting govern) → rutting CDF 2.07 — thicken

3-layer section, dual wheel at 20 in spacing, q 100 psi, a 5 in

single-wheel 942 µε → dual-gear 1132 µε subgrade strain (1.20× amplification)

dual gear 150 kN/wheel, 1.4 MPa, 125 mm AC / 400 mm base, 1200 dep/yr × 20 yr

subgrade strain → coverages-to-failure (verified Bleasdale) → CDF vs 1.0 adequacy

narrow-body (130 kN, 3000 dep/yr) + wide-body (250 kN dual-tandem, 400 dep/yr), 20 yr

Σ-aircraft CDF; the heavy wide-body governs despite fewer departures

125 mm AC, εt from Burmister, S 3447 MPa, Va 7 %, Vb 11 %, 1200 dep/yr × 20 yr

PV → Nf (0.4801·PV⁻⁰·⁹⁰⁰⁷) → HMA CDF vs 1.0 (secondary to the governing subgrade CDF)

IRI₀ 63, RD 0.3 in, FC 5 %, TC 200 ft/mi, age 10 yr, wet frost-prone subgrade

site factor 368 → IRI 84 in/mi (1.33 m/km) — good ride

250 mm slab, MR 4.5 MPa, k 30 MPa/m, 9 kip wheel, 5e7 reps

Westergaard edge stress → σ/MR → Nf → ~20 % slabs cracked

250 mm slab, E 28 GPa, k 30 MPa/m, 40 kN wheel @ 0.7 MPa, edge load, MR 4.5

ℓ 1056 mm · σ_edge 1.44 MPa (FoS 3.1) · FE deflection 0.64 mm · corner 0.38 mm

Cold continental (Dfa) zone, Northern hemisphere

Monthly temps −9→21 °C, precip 600 mm, freezing index 450 °C·days — feeds the distress drivers

280 mm slab, MR 4.5, k 40, 5×10⁷ reps, 20 yr

Month-by-month load + curling → 6.6 % slabs cracked (within terminal); ΔT=0 matches the single-pass check

3-aircraft mix (B737/A320/B777), 20 yr, 60 MPa subgrade

Required AC 335 mm; B777-300 governs (heaviest gear dominates the subgrade CDF)

4" P-401 / 8" P-403 / 12" P-209 / design P-154, CBR 5, 4-aircraft mix (B737-800/A321/EMB195/CRJ700), 20 yr

FAAModulus sublayer moduli + Bleasdale failure → P-154 = 10.6 in (FAARFIELD 10.1); A321-200 governs

P-501 R=600 psi, k=100 pci, 4-aircraft mix, 20 yr

Westergaard edge stress + Rollings SCI failure → slab = 17.9 in (FAARFIELD FE 17.14); A321-200 governs

Single-axle spectrum 40–120 kN, 1M axles

Truck factor 1.54 → 1.54M ESALs; heavy tail dominates

150 mm AC / 300 mm base / 60 MPa subgrade, 1e6 axles/yr, 20 yr, moderate climate

month-by-month → total rut 21 mm (AC 15 + subgrade 5), fatigue 22 %, IRI 1.66 m/km (NCDOT-validated band)

IRI₀ 63, 10 % cracked, 5 % spalled, 2 in/mi faulting, age 20 yr

site factor + distress → IRI 79 in/mi (good ride)

age 20 yr, 6 % air, f'c 28 MPa, 50 freeze-thaw/yr, 250 mm slab, w/c 0.45

durability scaling factor → ~5 % joints spalled (feeds JPCP IRI)

250 mm slab, aggregate base, undowelled, erodibility 3, curling 0.024 in

joint LTE 52 % · DE 0.079 lb/in · curling faulting potential 0.126 in

accumulated transverse fatigue damage DIPO = 1, crack spacing 48 in

PO = 216.8421/(1+33.158·1^-0.589) → 6.4 punchouts/mi

mild climate ΔT 25 °C vs cold ΔT 60 °C, 150 mm AC

mild ~6 ft/mi (negligible) → cold ~200 ft/mi (severe) low-temp cracking

150 mm AC, hot climate (mean 20 °C ± 18), 1e7 reps, β1r 0.5

monthly-incremental asphalt rut ~0.6 in — realistic (single-shot gives absurd 0.5 in/sublayer)

fine subgrade MR 60 MPa, Wc 15 %, 1e7 reps over 1.5 m compressible depth

εo/εr 71, depth-integrated subgrade rut ~0.2 in (wetter subgrade → more)

SO3 0.6 %, SO4 1.5 g/L, Cl 500 mg/L, pH 6.5

Class 3 (Severe) → SRPC, 330 kg/m³, w/c 0.50, cover 50 mm

FoS profile, Dr 50 %

Post-liquefaction settlement 92 mm

Free-face 5 m, T15 3 m

Ground displacement 0.9 m

(N1)60cs 8, σ′v0 100 kPa, driving shear 12 kPa

Sr/σ′v0 0.09 → Sr 9 kPa, flow-slide FoS 0.75 < 1 (mitigate)

0.8 m columns, 2 m grid, a_s 0.13

n 2.8 (Priebe) → settlement reduced to 38 %

Loose sand Dr 45 %

Dr → 75 % at 2.6 m probe spacing

0.8 m columns, a_s 0.25

Composite stiffness → settlement to 45 %

50 msa, subgrade CBR 8 %, 90 % reliability

BC 50 + DBM 130 + 553 granular = 733 mm; ε checked

30 MSA, 98-pctile axle stress

Slab 280 mm, fatigue + erosion < 100 %

W18 5×10⁶, MR 10 ksi

SN 4.2 → layer thicknesses

W18 30×10⁶, S′c 4.5 MPa, k 40 MPa/m, J 3.2, R 90 %

PCC slab D ≈ 302 mm (serviceability ΔPSI 2.0)

8 mm/blow penetration rate

CBR ≈ 14 % → subgrade acceptance band

Building footprint, 8 m grid

12 boreholes, depths to 1.5 × B below founding

Gs 2.70, γd 16 kN/m³, w 12 %

e 0.655, n 0.396, Sr 49 %, γ 17.9 / γsat 19.9 / γ′ 10.1 kN/m³

70 % fines, LL 45, PL 22 (PI 23)

USCS CL (lean clay), AASHTO A-7-6, above the A-line

w 30, LL 45, PL 22, clay 30 %

PI 23, I_L 0.35 (medium/firm), activity 0.77 (normal)

σ1 150, σ3 50 kPa, c′ 0, φ′ 30°

p 83.3, q 100, s 100, t 50, η = M = 1.2 — at failure

3 layers: 2 m@1e-5, 3 m@1e-7, 1 m@1e-6 m/s

k_h 3.6×10⁻⁶, k_v 1.9×10⁻⁷ m/s, anisotropy 18.5×

k 1e-5 m/s, H 4 m, N_f 4, N_d 12, 50 m wide

q 1.33×10⁻⁵ m³/s/m → 57.6 m³/day total, exit gradient 0.22

40 × 20 m pit, k 1e-4 m/s, drawdown 5 m, H 12 m, 10 wells

r_e 16 m, R 150 m → 1,151 m³/day total (115 per well), drawdown cone plotted

Q 1000 m³/day, r 30 m, Δs 0.5 m/cycle, t₀ 0.01 day, b 10 m

T 367 m²/day, S 0.0092, k 36.6 m/day

Base D15/D85 0.05/0.5 mm, filter D15/D50/D85 0.6/2/8 mm

Retention 1.2 ≤ 4 ✓, permeability 12 ≥ 4 ✓ → filter acceptable

D10 0.1, D30 0.3, D60 0.6 mm (sand)

C_u 6.0, C_c 1.5 → well graded

D10 0.2 mm, e 0.6, C 0.3 cm²

h_c 0.25 m (25 cm), suction 2.45 kPa

k 1e-5 m/s, Δh 3 m over L 10 m, n 0.4, A 2 m²

i 0.30, v 3×10⁻⁶, v_s 7.5×10⁻⁶ m/s, Q 6×10⁻⁶ m³/s

z 5 m, WT 2 m, γ 18 / γ_sat 20 kN/m³

σ_v 96, u 29.4, σ′_v 66.6 kPa (full profile plotted)

σ3 50 kPa, c 10 kPa, φ 30°

σ1f 184.6 kPa, q_u 34.6, plane 60°, circle tangent to envelope

Δσ₁ 200, Δσ₃ 50 kPa, A 0.5, B 1.0

Δu 125 kPa (contractive), Ā 0.5, Δσ′₁ 75 / Δσ′₃ −75 kPa

qc / fs depth profile

SBT zones, φ′ 36° (Kulhawy-Mayne), Dr, su

t50 100 s, 10 cm² cone, Ir 100, u2

ch 246 m²/yr (T50* 0.245); kh from mv

3 CD tests σ'3 100/200/300, σ'1 3× σ'3

M 1.20 → φ' 30°, c' 0 (R² 1.0)

z 5 m, qt 5 MPa, fs 50 kPa, γ 20, GWT 0

iterated n 0.64 → Ic 2.01 (SBT 6, sand-like)

H 5 m, γ 20, crest a 5 m, 2H:1V, z 10 m

q 100 kPa, I 0.395 → Δσv 79 kPa (centreline)

γ 18, φ 30°, surface deadman h 2 m, T 40 kN/m

Kp−Ka 2.67 → T_ult 96 kN/m, FoS 2.4 (OK)

ch 2 m²/yr, U 90% in 6 mo, dw 66 mm, s 2, kh/ks 2

required triangular spacing ≈ 1.05 m (n ≈ 17)

KL/r 100, fy 250, class b, Ae 6000 mm²

χ 0.52 → fcd 118 MPa → Nd 709 kN

Mu 225 kN·m, b 300, d 500, M25, Fe415

Mu,lim 259 → Ast 1495 mm² (singly OK)

N 1000 kN, Lu 3 m, EI 40 MN·m², clay kh 10 MN/m³

zf 1.98 m → Pcr 3982 kN → δ 1.34 (FoS 4.0)

Field N 19/23/33, σ′v 144–198 kPa, Peck Cn

Design N 17/19/26 with overburden + dilatancy + N60

Corrected N 21, silty sand, σ′v 160 kPa

φ′, cu, Es, Dr, γ, qc — min/mean/max envelope + recommended

p0 300, p1 800, u0 50, σ′v 100 kPa

ID 2.0 (sand), KD 2.5, M 20.9 MPa, φ′ 33.5°

ple* 1.0 MPa, EM 10 MPa, 2 m square in sand

kp 1.28, q_net 1,285 kPa, settlement 7.5 mm

Sand-replacement on a compacted layer

γ_d 17.8 kN/m³ → 96 % of MDD ✓

Wenner array, 4 spacings

ρ 22 Ω·m → soil corrosivity class

LL 50, w_n 35, e0 0.95, Gs 2.70

Cc 0.29 (mean of 5 correlations), Cr 0.06

k 1.5 W/m·°C, ρd 1700, w 15 %, F 600 °C·days

Frost line 1.22 m (Modified Berggren, λ 0.9)

t₅₀ 10 min, H_dr 10 mm, m_v 0.2 (Casagrande)

c_v 1.04 m²/yr (3.3×10⁻⁸ m²/s), k 6.4×10⁻¹¹ m/s

e–log σ′ curve, break at 100 kPa, σ′v0 50

σ′p 100 kPa, OCR 2.0, Cc 0.25, Cr 0.05

σci 50 MPa, mi 10, GSI 45, RQD 70

RMR 62 (class II), Q 8.3, mb 1.40, s 0.0022

r0 5 m, p0 10 MPa, c 1 MPa, φ 30°, unsupported

p_cr 4.13 MPa, plastic radius 9.2 m, convergence 77 mm

FSI 80 %, PI 45, swell pressure 220 kPa

Severity high → under-reamed piles / CNS layer

2 m active zone, Cs 0.08, p_s 200 kPa, σ'_final 50

ΔH 50.7 mm (high) — surcharge 200 kPa to suppress

h0 20 mm, 19 → 17.5 mm on wetting at 200 kPa

I_c 7.5 % → moderately severe collapse

—

—

Casagrande LL + rolled PL

LL 42, PL 20 → PI 22, USCS CL

Mass retained per sieve

Cu 8, Cc 1.2 → well-graded sand (SW)

Hydrometer readings vs time

18 % clay, 22 % silt fraction

4-mass pycnometer

G 2.67 at 27 °C

Flakiness + elongation gauges

Flakiness 28 %, elongation 22 %

Mercury displacement

SL 14 %, shrinkage ratio 1.8

—

—

Compaction at 5 moisture points

OMC 14 %, MDD 1.82 g/cc

Soaked 4-day, 2.5 / 5.0 mm

CBR 8 % (governs at 2.5 mm)

e_max / e_min, field e

Dr 65 % → medium dense

Single specimen to failure

qu 110 kPa → su 55 kPa, sensitivity 3

3 cells, undrained

c_u 48 kPa, φ_u 0°

3 cells, CU + pore pressure

c′ 8 kPa, φ′ 29°, A_f 0.6

3 cells, drained

c′ 5 kPa, φ′ 32°

3 normal stresses

c′ 6 kPa, φ′ 31°

Peak + remoulded torque

su 52 → 17 kPa, sensitivity 3.1

3 stages to large displacement

φ′r 27.5°, c′r 0 (residual)

e-log p loading

Cc 0.32, Cv 2.4 m²/yr, pc′ 120 kPa

Constant rate of strain

Cv(σ′) curve + mv, continuous

Falling-head

k 3×10⁻⁷ m/s

CSR vs cycles to liquefaction

Liquefies in 14 cycles at CSR 0.2

Torsional resonance

Gmax 95 MPa, damping 1.8 %

—

—

—

—

—

—

Diametral on core

Is(50) 3.2 MPa → UCS ≈ 77 MPa

2-cycle wet-dry

Id2 96 % → durable rock

Free-swell index

FSI 80 % → high expansivity

Constant-volume oedometer

Swell pressure 220 kPa

pH · sulphate · chloride · organic

pH 7.8, SO₄ 1,200 ppm → moderate exposure

Loss on ignition at 440 °C

OC 20 % → organic soil

Flow at 50 mm head, dark effluent

Class D1 → highly dispersive

—

—

—

—

—

—

—

—

—

—

—

—

—

—

—

—

—

—

—

—

—

—

—

—

—

—

—

—