Compiled formulas (GEOTECH)

e(void ratio)=

Porosity, n=

Degree of Saturation, S=

Relationship between G, w, s and e

Moist Unit or bulk unit weight, Ym

Dry unit weight, Yd

Saturated unit weight, Ysat

Critical hydraulic gradient, icr

RELATIVE DENSITY OR DENSITY INDEX (Dr)

RELATIVE COMPACTION (R)

COEFFICIENT OF UNIFORMITУ

COEFFICIENT OF GYRATION

SUITABILITY NUMBER

Suitability rating index

SORTING COEFFICIENT

SHRINKAGE LIMIT (SL)

LOG

SIEVE ANALYSIS

OPENING DIAMETER

LIN

SIEVE ANALYSIS

PERCENT FINER

Shrinkage Ratio (SR)

specific gravity of soil solids (Gs​)

ATTERBERG LIMITS

LIQUID LIMIT (LL)

3.2 mm DIAMETER

PLASTIC LIMIT (PL)

LL-PL

PLASTICITY INDEX

LIQUIDITY INDEX

CONSISTENCY INDEX

ACTIVITY OF CLAY, Ac

• Particles retained on No. 4 sieve (4.75 mm)

Coarse Fraction: Material retained on the No. 200 sieve

Gravel:________

Particles that pass No. 4 (4.75 mm) but are retained on No. 200 (0.075 mm)

Coarse Fraction: Material retained on the No. 200 sieve

Sand:__________

• Silt and Clay: < 0.075 mm

Fine Fraction: Material passing No. 200 sieve

> 2 mm

USDA Soil Texture Classification (by particle size)

Gravel

• 2 mm to 0.05 mm

USDA Soil Texture Classification (by particle size)

Sand

• 0.05 mm to 0.002 mm

USDA Soil Texture Classification (by particle size)

Silt

• < 0.002 mm

USDA Soil Texture Classification (by particle size)

Clay

AASHTO Soil Classification System

Group Index (GI) Formula

A-1, A-3, A-2-4, A-2-5 (Good quality soils)

GI = 0

A-2-6, A-2-7 (Intermediate soils)

GI = Partial

• A-4, A-5, A-6, A-7 (Poor quality soils)

GI = Full

Velocity (v)

Hydraulic Gradient (i)

Seepage or Interstitial Velocity (v_s)

Seepage Force (SF)

Discharge (Q)

Constant Head Test (k)

Falling Head Test (k)

Pumping Test (Unconfined Aquifer)

Pumping Test (Confined Aquifer)

Transmissivity (T)

Flow Nets Discharge (Q)

Uplift Pressure, u

Parallel Flow – Equivalent Hydraulic Conductivity

Perpendicular Flow

Capillary Rise (h)

Effective Stress (P_e)

Primary Consolidation Settlement (ΔH)

Overly Consolidated Settlement

Compression Index (Cₙ)

Swell Index (Cₛ)

Overconsolidation Ratio (OCR)

Coefficient of Compressibility (aᵥ)

Coefficient of Volume Compressibility (mᵥ)

Coefficient of Consolidation (Cᵥ)

Hydraulic Conductivity (k)

Positive

Mohr’s Circle Sign Convention

Compression

Counter-clockwise is positive

Mohr’s Circle Sign Convention

Shear

Triaxial Test – Angle of Failure (θ)

Rankine Earth Pressure – Active Pressure (Kₐ)

Rankine Earth Pressure – Passive Pressure (Kₚ)

Rest Earth Pressure (K₀)

Bearing Capacity – General Shear Failure

Stress Increase (ΔP) from Point Load

Stress Increase (ΔP) – Uniform Load

Boussinesq Equation – Point Load

Effect of Water Table

General Shear Failure – Strip Foundation

Square Footing – Ultimate Bearing Capacity

Circular Footing – Ultimate Bearing Capacity

Effect of Water Table – Case 1

Effect of Water Table – Case 2

Effect of Water Table – Case 3

Pile in Sand Layer

Pile in Clay Layer

Total Pile Capacity (in Clay or Sand)

Tip Capacity in Clay

Group Efficiency of Piles

Critical Depth (D_c)

• For loose sand:

Critical Depth (D_c)

For dense sand:

Braced Cut – Depth of Struts (h)

Infinite Slope – Factor of Safety (FS) Without Seepage

Infinite Slope – Factor of Safety With Seepage

Fixed Slope – Factor of Safety

Maximum Height for Critical Equilibrium (Hcᵣ)

Stability Number (m)

Stability Factor

FACTOR OF SAFETY AGAINST SLIDING