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The following calculations are used in this test:

 

Deformation

 

The axial deformations can be specified directly or using deformation dial readings. When using dial readings they are converted to actual deformations using a dial constant.

 

Da = (Ra - Rai) * ADC                        

 

where,

Da        = Axial deformation

Ra        = Axial dial reading

Rai        = Initial axial dial reading

ADC        = Axial dial constant

 

 

Axial Load

 

The Axial loads can be specified directly or using readings from a load ring. When using readings from a load ring the readings are converted to loads either using load ring constants or a linear equation.

 

Load Ring Constant

 

If (R - R0) < Crossover        Pa = (R - R0) * LRC1                

 

If (R - R0) > Crossover        Pa = Crossover * LRC1 + (R - R0 - Crossover) * LRC2

 

Linear

 

Pa = M * (R - R0) + C

 

where,

Pa        = Axial load

R        = Load dial reading

R0        = Initial load dial reading

LRC1        = Load ring constant 1

LRC2        = Load ring constant 2

M        = Linear multiplier

C        = Linear constant

 

 

Axial Strain

 

εa = Da / h        

 

where,

εa        = Axial strain

Da        = Axial deformation

h        = Saturated height of specimen, if not specified uses h0

h0        = Initial height

 

 

Deviator Stress

 

σd = Pa / A  - ΔσRM - ΔσFP

 

where,

σd        = Axial stress

Pa        = Axial load

A        = Cross-sectional area

ΔσRM        = Rubber membrane correction, only applied if greater than 5% of σd (see below)

ΔσFP        = Filter paper correction, only applied if greater than 5% of σd (see below)

 

 

Minor Stress

 

σ3 = CP - Bp

 

where,

σ3        = Minor stress

Cp        = Confining pressure

Bp        = Back pressure

 

 

Major Stress

 

σ1 = σd + σ3

 

where,

σ1        = Major stress

 

 

Peak Compressive Strength

 

Compressive strength = maximum σd

 

 

Saturated Volume

 

If assuming 100% saturation,

 

Vsat = (Vs + Ms * wi - ΔV)

 

or using COE Uniform Strain method

 

Vsat = h * A0 * [1 - 2 * (h0 - h) / h0 ]

 

where,

Vsat        = Saturated volume

Vs        = Volume of solids = Ms / (SG * ρw)

Ms        = Mass of solids = ρd * V0

A0        = Initial cross-sectional area = π * d02 / 4

V0        = Initial volume =  A0 * h0

SG        = Specific gravity

ρd        = Initial dry density

ρw        = Density of water (1.0 g/cm3)

ΔV        = Saturated volume change

wi        = Initial water content

d0        = Initial diameter

 

 

Cross-sectional Area

 

If calculating saturated results and saturated height specified,

 

A = Vsat / h

 

or else,

 

A = A0 / (1 - εa)

 

where,

A        = Cross-sectional area

 

 

Rubber Membrane Correction

 

ΔσRM = 4 * Em * tm * εa / Dc

 

where,

ΔσRM        = Rubber membrane correction

Em        = Young's modulus

tm        = Membrane thickness

Dc        = Diameter after consolidation = (4 * Ac / π)½

 

 

Filter Paper Correction

 

ΔσFP = KFP * PFP / Ac                                For εa greater than 2%

 

ΔσFP = 50 * εa * KFP * PFP / Ac                        For εa less than 2%

 

where,

ΔσFP        = Filter paper correction

KFP        = Load carried per unit length of perimeter covered by filter paper

PFP        = Perimeter covered by filter paper = %C * P

%C        = Percentage of perimeter covered

P        = Perimeter of specimen = π * d0

 

 

Water Content

 

wi (%) = 100 * (Mbwt - Mbdt) / (Mbdt - Mbt)                Initial

 

or if Mbwt and Mbdt not specified,

 

wi (%) = 100 * [Mw - (Madt - Mat)] / (Madt - Mat)        Initial

 

ws (%) = 100 * (Vsat - Vs) / Ms                        Saturated

 

wf (%) = 100 * (Mawt - Madt) / (Madt - Mat)        Final

 

where,

wi        = Initial percentage water content

ws        = Saturated percentage water content

wf        = Final percentage water content

Mbwt        = Mass of tare and wet specimen before test

Mbdt        = Mass of tare and dry specimen before test

Mbt        = Mass of tare used before test

Mawt        = Mass of tare and wet specimen after test

Madt        = Mass of tare and dry specimen after test

Mat        = Mass of tare used after test, if not specified uses mass of tare before test

Mw        = Wet sample mass

 

 

Dry Density

 

ρi = Mw / V0 / (1+ wi/100)                        Initial

 

ρs = Ms / Vsat                                        Saturated

 

where,

ρi        = Initial dry density

ρs        = Saturated dry density        

 

 

Dry Unit Weight

 

γi = ρi * γw                                        Initial

 

γs = ρs * γw                                        Saturated

 

where,

γi        = Initial dry unit weight

γs        = Saturated dry unit weight

γw        = Unit weight of water (9.807 kN/m3)

 

 

Saturation

 

Si (%) = 100 * Vwi / Vvi                                Initial

 

Ss (%) = 100 * Vws / Vvs                        Saturated

 

where,

Si        = Initial saturation

Ss        = Saturated saturation

Vwi        = Initial volume of water in sample = (Mw - Ms) / ρw

Vws        = Saturated volume of water in sample = [Vsat * ρs * (1 + ws/100) - Ms] / ρw

Vvi        = Initial volume of voids = V0 - Vs

Vvs        = Saturated volume of voids = Vsat - Vs

 

 

Void Ratio

 

ei = Vvi / Vs                                        Initial

 

es = Vvs / Vs                                        Saturated

 

where,

ei        = Initial void ratio

es        = Saturated void ratio