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Geotechnical Engineering Formulas
Void Ratio (General Formula) - correct answer e = Vv/Vs Void Ratio (Given n) - correct answer e=n/1-n Porosity (General Formula) - correct answer n=Vv/Vt Porosity (Given e) - correct answer n=e/1+e Degree of Saturation - correct answer S=Vw/Vv Moisture/Water Content - correct answer w=Ww/Ws or Mw/Ms Total Weight of Soil Sample - correct answer Wt=Ww+Ws Volume of Voids - correct answer Vv=Va+Vw Total Volume of Soil Sample - correct answer Vt=Vv+Vs Dry Unit Weight (Given Gs&e) - correct answer γd=Gsγw/1+e Dry Unit Weight (Given γm&w) - correct answer γd=γm/1+w Moist/Natural Unit Weight (Given Gs,e,w,&S) - correct answer γm=(Gs+Se)γw/1+e or
γm=(Gs+Gsw)γw/1+e Saturated Unit Weight (Given Gs&e) - correct answer γsat=(Gs+e)•γw/1+en Unit Weight - correct answer γ=W/V Submerged/Buoyant Unit Weight (Given Gs&e) - correct answer γ'=(Gs-1)•γw/1+e Submerged Unit Weight (Given Saturated Unit Weight) - correct answer γ'=γsat-γw Relationship Between S,e,w,&Gs - correct answer Se=wGs Bulk Specific Gravity - correct answer G=γ/γw Specific Gravity of Solids - correct answer Gs=γs/γw Critical Hydraulic Gradient (Based on Unit Weights) - correct answer Icr=γ'/γw Critical Hydraulic Gradient (Given Gs&e) - correct answer Icr=(Gs-1)/1+e Air Content (Given Volume) - correct answer Ac=Va/Vt Air Content - correct answer Ac=n(1-S) Air Void Ratio (Given Volume) - correct answer Na=Va/Vv
Sn Rating (30-50) - correct answer Poor Relationship Between In-Situ Volume of Soils and Void Ratio - correct answer Vt1/(1+e1)=Vt2/(1+e2) Water Content (Given Natural Mass and Dry Mass) - correct answer w=(M1-M2)/M Change in Water Content (Based on Volume) - correct answer ∆w=(V1-V2)•ρw/M Shrinkage Limit - correct answer SL=w-∆w Shrinkage Limit (Given Gs&e) - correct answer SL=100e/Gs Shrinkage Ratio - correct answer SR=M2/V2•ρw Specific Gravity of Solids (Given SR and SL - correct answer GS= 1/(1/SR - SL/100) Plastic Limit - correct answer PL=w Liquid Limit - correct answer LL=w Liquidity Index - correct answer LI=(w-PL)/(LL-PL) Plasticity Index - correct answer PI=LL-PL Consistency Index - correct answer CI=(LL-w)/(LL-PL)
Activity Classification (of Clay) - correct answer Ac=PI/%Clay Group Index - correct answer GI=(F200-35)(0.005LL) +0.01(F200-15)(PI-10) Liquid Limit (Cup/Casagrande Apparatus) - correct answer LL=25 blows Liquid Limit (Falling Cone Apparatus) - correct answer LL=20mm Penetration USDA Soil Classification Distribution - correct answer Distribution=%Classification•100/100%•%Gravel Retained Gravel - correct answer G/CF = (100-F4)/(100- F200) Diameter of Soil Passing - correct answer Logarithmic Interpolation Between Diameter and Percent Passing Discharge/Rate of Flow - correct answer Q=Av Discharge/Superficial Velocity - correct answer v=ki Seepage/Interstitial Velocity - correct answer vs=ki/n Seepage Force - correct answer j=iγw Transmissivity - correct answer Tv=kt Hydraulic Conductivity/Coefficient of Permeability (Constant Head Test) - correct answer k=Vl/Aht
Compression Index (Given LL) - correct answer Cc=0.009(LL-
Compression Index (Given e&P) - correct answer Cc=(e1- e2)/log(P2-P1) Over-consolidation Ratio - correct answer OCR=Pc/Po Normally Consolidated Settlement - correct answer Sc=(CcH)/(1+e) • log((Po+∆P)/Po) Settlement In Soil if PfPc - correct answer Sc=(CsH)/(1+e) • log(Pc/Po) + (CcH)/(1+e) • log ((Po+∆P)/Pc) Coefficient of Compressibility - correct answer av=(e1-e2)/(P2-P1) Coefficient of Volume Compressibility - correct answer mv=av/1+ē Note:ē-Average Void Ratio Coefficient of Consolidation - correct answer Cv=(Hdr²•Tv)/T Note: If sample is drained on both sides, Hdr is divided by 2 Hydraulic Conductivity (Using Coefficients) - correct answer k=Cv•Mv•γw
Flow Channels - correct answer Horizontal Lines Pressure Drops - correct answer Vertical Lines Angle of Failure in Shear - correct answer θ=45+(φ/2) ∆σ - correct answer Additional Stress Deviator Stress Minimum Principal Stress Confining Pressure Lateral Pressure Radial Stress Cell Pressure Chamber Pressure - correct answer σ Maximum Axial Stress Maximum Normal Stress - correct answer σ Normal Stress - correct answer σ Shear Stress - correct answer τ Relation of Cohesion with Pressure - correct answer q=Cu/2=C Coefficient of Active Soil Pressure - correct answer ka=(1- sinφ)/(1+sinφ) if β= Coefficient of Active Soil Pressure - correct answer ka= cosβ(cosβ-√(cos²β-cos²φ))/(cosβ+√(cos²β-cos²φ))
Boussinesq Equation for Uniform Load - correct answer ∆P=2qz³/(π(z²+r²))² Terzaghi's Circular General Shear Failure - correct answer qult=1.3cNc+qNq+0.3γBNγ Terzaghi's Square General Shear Failure - correct answer qult=1.3cNc+qNq+0.4γBNγ Terzaghi's Strip General Shear Failure - correct answer qult=cNc+qNq+0.3γBNγ Terzaghi's Circular Local Shear Failure - correct answer qult=1.3c'Nc'+qNq'+0.3γBNγ' Terzaghi's Square Local Shear Failure - correct answer qult=1.3c'Nc'+qNq'+0.4γBNγ Tergazhi's Strip Local Failure - correct answer qult=c'Nc'+qNq'+0.5γBNγ Capacity of Driven Piles in Sand (Tip) - correct answer Qutip=qNqAtip Capacity of Driven Piles in Sand (Friction) - correct answer Quf=KAPtan∝ Capacity of Driven Piles in Sand (Ultimate and Allowable) - correct answer Qu=Qutip+Quf Qall=Qu/FS Capacity of Driven Piles in Clay Layer (Tip) - correct answer Qutip=cNcAtip
Capacity of Driven Piles in Clay (Friction) - correct answer Quf=CuP∝L Capacity of Driven Piles in Clay (Ultimate and Allowable) - correct answer Qu=Qutip+Quf Qall=Qu/FS Pressure in Braced System (Sand) - correct answer 0.65ka•γH Pressure in Braced System (Soft to Medium Clay) - correct answer p=γH-4Cu when γH/Cu > 4 Pressure in Braced System (Stiff Clay) - correct answer 0.2γH to 0.4γH when γH/Cu > 4 Fixed Slope - Force due to Friction - correct answer Ff=μN=μW=Wcosθtanφ Fixed Slope - Force due to Cohesion - correct answer Fc=cAc=cLw Fixed Slope - Factor Safety - correct answer FS= (Ff+Fc)/Wsinθ Unstable Soil - Factor of Safety neglecting Seepage - correct answer FS= (C/γHsinβcosβ) + (tanφ/tanβ) Unstable Soil - Factor of Safety considering Seepage - correct answer FS= (C/γsatHsinβcosβ) + (γ'tanφ/γsattanβ)
