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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 / hc
where,
εa = Axial strain
Da = Axial deformation
hc = Consolidated height of specimen
Deviator Stress
σd = Pa / A - ΔσRM - ΔσFP
where,
σd = Axial stress
Pa = Axial load
A = Cross-sectional area (see below)
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
The calculation of the saturated volume will depend primarily whether the saturated diameter was specified and on the cross-section method selected.
Vsat = π * hs * ds2 / 4 Saturated diameter specified
Vsat = V0 - ΔVsat ASTM Method A
Vsat = Vwater + Vsolid + ΔVcon ASTM Method B
Vsat = Vsolid + Vvoid + ΔVcon ASTM Method B with consolidated saturation estimate
Vsat = hs * [1 - 2*(h0 - hs) / hs] * A0 COE Uniform Strain
Vsat = Vsolid + Ms * wi - ΔVsat COE Saturation Assumed
where,
Vsat = Saturated volume
Vsolid = 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
Vwater = Final volume of water = wf * Ms / 100
Vvoid = Final volume of voids = (wf * Ms) / Sest
Sest = Estimated percentage consolidated saturation
ΔVsat = Saturated volume change
ΔVcon = Consolidated volume change
hs = Saturated height
ds = Saturated diameter
wi = Initial water content
d0 = Initial diameter
wf = Final percentage water content
Consolidated Volume
The calculation of the consolidated volume will depend primarily whether the consolidated diameter was specified and on the cross-section method selected.
Vcon = π * hc * dc2 / 4 Consolidated diameter specified
Vcon = V0 - ΔVcalc - ΔVcon ASTM Method A
Vcon = Vwater + Vsolid ASTM Method B
Vcon = Vsat - ΔVcon ASTM Method B with consolidated saturation estimate
Vcon = hc * [1 - 2*(h0 - hc) / h0] * A0 COE Uniform Strain
Vcon = Vsat - ΔVcon COE Saturation Assumed
where,
Vcon = Consolidated volume
ΔVcalc = Calculated change in saturated volume = 3 * V0 * (h0 - hs) / h0
hc = Consolidated height
dc = Consolidated diameter
Cross-sectional Area
A = Acor / (1 - εa)
where,
A = Cross-sectional area
Acor = Corrected consolidated cross-sectional area = (Vcon - ΔVb) / hc
ΔVb = Outflow buret volume = Vb - Vbi
Vb = Buret volume reading
Vbi = Initial buret volume reading
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
The calculation of the water content volume will depend primarily whether the saturated diameter is specified and on the cross-section method selected.
wi (%) = 100 * (Mbwt - Mbdt) / (Mbdt - Mbt) Initial
wi (%) = 100 * [Mw - (Madt - Mat)] / (Madt - Mat) Initial if Mbwt and Mbdt not specified
ws (%) = 100 * (Vsat - Vs) / Ms Saturated diameter specified
ws (%) = 100 * (Ms * wf + ΔVcon) / Ms Saturated ASTM Method A and B
ws (%) = 100 * (wi - ΔVsat / Ms) Saturated COE Uniform Strain
ws (%) = 100 * (Vsat - Vsolid) / Ms Saturated COE Saturation Assumed
wc (%) = 100 * (ws - ΔVcon / Ms) Consolidated ΔVcon specified
wc = wf Consolidated ΔVcon not specified
wf (%) = 100 * (Mawt - Madt) / (Madt - Mat) Final
where,
wi = Initial percentage water content
ws = Saturated percentage water content
wc = Consolidated 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
ρc = Ms / Vcon Consolidated
where,
ρi = Initial dry density
ρs = Saturated dry density
ρc = Consolidated dry density
Dry Unit Weight
γi = ρi * γw Initial
γs = ρs * γw Saturated
γc = ρs * γw Consolidated
where,
γi = Initial dry unit weight
γs = Saturated dry unit weight
γc = Consolidated dry unit weight
γw = Unit weight of water (9.807 kN/m3)
Saturation
Si (%) = 100 * Vwi / Vvi Initial
Ss (%) = 100 * Vws / Vvs Saturated
Sc (%) = 100 * Vwc / Vvc Consolidated
where,
Si = Initial saturation
Ss = Saturated saturation
Sc = Consolidated saturation
Vwi = Initial volume of water in sample = (Mw - Ms) / ρw
Vvi = Initial volume of voids = V0 - Vs
Vws = Saturated volume of water in sample = [Vsat * ρs * (1 + ws/100) - Ms] / ρw
Vvs = Saturated volume of voids = Vsat - Vs
Vwc = Consolidated volume of water in sample = [Vcon * ρc * (1 + wc/100) - Ms] / ρw
Vvc = Consolidated volume of voids = Vcon - Vs
ρw = Density of water (1.0 g/cm3)
Void Ratio
ei = Vvi / Vs Initial
es = Vvs / Vs Saturated
ec = Vvc / Vs Consolidated
where,
ei = Initial void ratio
es = Saturated void ratio
ec = Consolidated void ratio